H. Mohamad and M. Oliver. High-order uniformly accurate time integrators for semilinear wave equations of Klein–Gordon type in the non-relativistic limit. arXiv:2008.05227, Preprint
M. Oliver and S. Vasylkevch. Non-negative matrix factorization with factorizable feature matrix. Preprint
M. Oliver and S. Vasylkevch. A new construction of modified equations for variational integrators, London Math. Soc. Lecture Note Ser., to appear. Preprint
E. Bagaeva, S. Danilov, M. Oliver, and S. Juricke (2024). Advancing eddy parameterizations: Dynamic energy backscatter and the role of subgrid advection and stochastic forcing, J. Adv. Model. Earth Syst. 16, e2023MS003972. DOI: 10.1029/2023MS003972, Preprint
M. Oliver and M. A. Tiofack Kenfack (2024). Deterministic and stochastic surrogate models for a slowly driven fast oscillator. SIAM J. Appl. Dyn. Syst. 23, 1090–1107. DOI: 10.1137/23M1602176, Preprint
A. Kutsenko, S. Danilov, S. Juricke, and M. Oliver (2024). On the relation between Fourier and Walsh–Rademacher spectra for isotropic random fields. Appl. Comput. Harmon. A. 68, 101603. DOI: 10.1016/j.acha.2023.101603, Preprint
M. Chouksey, C. Eden, G. T. Masur, and M. Oliver (2023). A comparison of methods to balance geophysical flows. J. Fluid Mech. 971, A2. DOI: 10.1017/jfm.2023.602, Preprint
G. T. Masur, H. Mohamad, and M. Oliver (2023). Quasi-convergence of an implementation of optimal balance by backward-forward nudging. Multiscale Model. Simul. 21, 624–640. DOI: 10.1137/22M1506018, Preprint
S. Juricke, K. Bellinghausen, S. D. Danilov, A. A. Kutsenko, and M. Oliver (2023). Scale analysis on unstructured grids: Kinetic energy and dissipation power spectra on triangular meshes. J. Adv. Model. Earth Syst. 15, e2022MS003280. DOI: 10.1029/2022MS003280, Preprint
Z. Darbenas, R. van der Hout, and M. Oliver (2023). Conditional uniqueness of solutions to the Keller–Rubinow model for Liesegang rings in the fast reaction limit. J. Differential Equations 347, 212–245. DOI: 10.1016/j.jde.2022.11.038, Preprint
Z. Darbenas, R. van der Hout, and M. Oliver (2023). Long-time asymptotics of solutions to the Keller–Rubinow model for Liesegang rings in the fast reaction limit. Ann. Inst. H. Poincaré Anal. Non Linéaire 39, 1413–1458. DOI: 10.4171/AIHPC/34, Preprint
Z. Darbenas and M. Oliver (2021). Breakdown of Liesegang precipitation bands in a simplified fast reaction limit of the Keller–Rubinow model. Nonlinear Differ. Equ. Appl. 28, Paper No. 4. DOI: 10.1007/s00030-020-00663-7, Preprint
H. Mohamad and M. Oliver (2021). Numerical integration of functions of a rapidly rotating phase. SIAM J. Num. Anal. 59, 2310–2319. DOI: 10.1137/19M128658X, Preprint
G. Özden and M. Oliver (2021). Variational balance models for the three-dimensional Euler–Boussinesq equations with full Coriolis force. Phys. Fluids 33, 076606. DOI: 10.1063/5.0053092, Preprint
I. Akramov and M. Oliver (2020). On the existence of solutions to a bi-planar Monge–Ampère equation. Acta Math. Sci. 40, 379–388. DOI: 10.1007/s10473-020-0206-6, Preprint
S. Juricke, S. Danilov, N. Koldunov, M. Oliver, D. V. Sein, D. Sidorenko, and Q. Wang (2020). A kinematic kinetic energy backscatter parametrization: From implementation to global ocean simulations. J. Adv. Model. Earth Syst. 12, e2020MS002175. DOI: 10.1029/2020MS002175, Preprint
S. Juricke, S. Danilov, N. Koldunov, M. Oliver, and D. Sidorenko (2020). Ocean kinetic energy backscatter parametrization on unstructured grids: Impact on global eddy-permitting simulations. J. Adv. Model. Earth Syst. 12, e2019MS001855. DOI: 10.1029/2019MS001855, Preprint
G. T. Masur and M. Oliver (2020). Optimal balance for rotating shallow water in primitive variables. Geophys. Astrophys. Fluid Dyn. 114, 429–452. DOI: 10.1080/03091929.2020.1745789, Preprint
Z. Darbenas and M. Oliver (2019). Uniqueness of solutions for weakly degenerate cordial Volterra integral equations. J. Integral Equ. Appl. 31, 307–327. DOI: 10.1216/JIE-2019-31-3-307, Preprint
S. Juricke, S. Danilov, A. Kutsenko, and M. Oliver (2019). Ocean kinetic energy backscatter parametrizations on unstructured grids: Impact on mesoscale turbulence in a channel. Ocean Model. 138, 51–67. DOI: 10.1016/j.ocemod.2019.03.009, Preprint
H. Mohamad and M. Oliver (2019). A direct construction of a slow manifold for a semilinear wave equation of Klein–Gordon type. J. Differential Equations 267, 1–14. DOI: 10.1016/j.jde.2019.01.001, Preprint
M. Oliver and S. Vasylkevych (2019). Geodesic motion on groups of diffeomorphisms with H1 metric as geometric generalised Lagrangian mean theory. Geophys. Astrophys. Fluid Dyn. 113, 466–490. DOI: 10.1080/03091929.2019.1639697, Preprint
G. Badin, M. Oliver, and S. Vasylkevych (2018). Geometric Lagrangian averaged Euler–Boussinesq and primitive equations. J. Phys. A: Math. Theor. 51, 455501. DOI: 10.1088/1751-8121/aae1cb, Preprint
H. Mohamad and M. Oliver (2018). Hs-class construction of an almost invariant slow subspace for the Klein–Gordon equation in the non-relativistic limit. J. Math. Phys. 59, 051509, 8. DOI: 10.1063/1.5027040, Preprint
M. Oliver (2018). An estimate on the Bedrosian commutator in Sobolev space. J. Inequal. Appl., Paper No. 348, 4. DOI: 10.1186/s13660-018-1940-3, Preprint
D. G. Dritschel, G. A. Gottwald, and M. Oliver (2017). Comparison of variational balance models for the rotating shallow water equations. J. Fluid Mech. 822, 689–716. DOI: 10.1017/jfm.2017.292, Preprint
G. A. Gottwald, H. Mohamad, and M. Oliver (2017). Optimal balance via adiabatic invariance of approximate slow manifolds. Multiscale Model. Simul. 15, 1404–1422. DOI: 10.1137/17M1124644, Preprint
M. Oliver (2017). Lagrangian averaging with geodesic mean. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 473, 20170558, 9. DOI: 10.1098/rspa.2017.0558, Preprint
M. Oliver and S. Vasylkevych (2016). Generalized large-scale semigeostrophic approximations for the f-plane primitive equations. J. Phys. A: Math. Theor. 49, 184001. DOI: 10.1088/1751-8113/49/18/184001, Preprint
C. Wulff and M. Oliver (2016). Exponentially accurate Hamiltonian embeddings of symplectic A-stable Runge–Kutta methods for Hamiltonian semilinear evolution equations. Proc. Roy. Soc. Edinburgh Sect. A 146, 1265–1301. DOI: 10.1017/S0308210515000852, Preprint
G. A. Gottwald and M. Oliver (2014). Slow dynamics via degenerate variational asymptotics. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 470, 20140460, 13. DOI: 10.1098/rspa.2014.0460, Preprint
A. Merico, G. Brandt, S. L. Smith, and M. Oliver (2014). Sustaining diversity in trait-based models of phytoplankton communities. Front. Ecol. Evol. 2, 59. DOI: 10.3389/fevo.2014.00059, Preprint
M. Oliver (2014). A variational derivation of the geostrophic momentum approximation. J. Fluid Mech. 751, R2 (10 pages). DOI: 10.1017/jfm.2014.309, Preprint
M. Oliver and C. Wulff (2014). Stability under Galerkin truncation of A-stable Runge–Kutta discretizations in time. Proc. Roy. Soc. Edinburgh Sect. A 144, 603–636. DOI: 10.1017/S0308210512002028, Preprint
O. Bokhove, V. Molchanov, M. Oliver, and B. Peeters (2013). On the rate of convergence of the Hamiltonian particle-mesh method. In Meshfree methods for partial differential equations VI (Vol. 89, pp. 25–43). Springer, Heidelberg. DOI: 10.1007/978-3-642-32979-1_2, Preprint
M. Çalık and M. Oliver (2013). Weak solutions for generalized large-scale semigeostrophic equations. Commun. Pure Appl. Anal. 12, 939–953. DOI: 10.3934/cpaa.2013.12.939, Preprint
M. Çalık, M. Oliver, and S. Vasylkevych (2013). Global well-posedness for the generalized large-scale semigeostrophic equations. Arch. Ration. Mech. Anal. 207, 969–990. DOI: 10.1007/s00205-012-0587-3, Preprint
V. Molchanov and M. Oliver (2013). Convergence of the Hamiltonian particle-mesh method for barotropic fluid flow. Math. Comp. 82, 861–891. DOI: 10.1090/S0025-5718-2012-02648-2, Preprint
M. Oliver and S. Vasylkevych (2013). Generalized LSG models with spatially varying Coriolis parameter. Geophys. Astrophys. Fluid Dyn. 107, 259–276. DOI: 10.1080/03091929.2012.722210, Preprint
M. Oliver and C. Wulff (2012). A-stable Runge–Kutta methods for semilinear evolution equations. J. Funct. Anal. 263, 1981–2023. DOI: 10.1016/j.jfa.2012.06.022, Preprint
M. Oliver and S. Vasylkevych (2011). Hamiltonian formalism for models of rotating shallow water in semigeostrophic scaling. Discrete Contin. Dyn. Syst. 31, 827–846. DOI: 10.3934/dcds.2011.31.827, Preprint
O. Bokhove and M. Oliver (2009). A parcel formulation of Hamiltonian layer models. Geophys. Astrophys. Fluid Dyn. 103, 423–442. DOI: 10.1080/03091920903286444, Preprint
G. A. Gottwald and M. Oliver (2009). Boltzmann’s dilemma: An introduction to statistical mechanics via the Kac ring. SIAM Rev. 51, 613–635. DOI: 10.1137/070705799, Local Copy
G. Gottwald, M. Oliver, and N. Tecu (2007). Long-time accuracy for approximate slow manifolds in a finite-dimensional model of balance. J. Nonlinear Sci. 17, 283–307. DOI: 10.1007/s00332-006-0804-2, Preprint
M. Oliver and O. Bühler (2007). Transparent boundary conditions as dissipative subgrid closures for the spectral representation of scalar advection by shear flows. J. Math. Phys. 48, 065502, 26. DOI: 10.1063/1.2668705, Preprint
O. Bokhove and M. Oliver (2006). Parcel Eulerian–Lagrangian fluid dynamics of rotating geophysical flows. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 462, 2575–2592. DOI: 10.1098/rspa.2006.1656, Preprint
M. Oliver (2006). Variational asymptotics for rotating shallow water near geostrophy: A transformational approach. J. Fluid Mech. 551, 197–234. DOI: 10.1017/S0022112005008256, Preprint
N. D. Aparicio, S. J. A. Malham, and M. Oliver (2005). Numerical evaluation of the Evans function by Magnus integration. BIT 45, 219–258. DOI: 10.1007/s10543-005-0001-8, Preprint
M. Oliver, M. West, and C. Wulff (2004). Approximate momentum conservation for spatial semidiscretizations of semilinear wave equations. Numer. Math. 97, 493–535. DOI: 10.1007/s00211-003-0488-3, Preprint
R. Ford, S. J. A. Malham, and M. Oliver (2002). A new model for shallow water in the low-Rossby-number limit. J. Fluid Mech. 450, 287–296. DOI: 10.1017/S0022112001006620, Preprint
M. Oliver (2002). The Lagrangian averaged Euler equations as the short-time inviscid limit of the Navier–Stokes equations with Besov class data in ℝ2. Commun. Pure Appl. Anal. 1, 221–235. DOI: 10.3934/cpaa.2002.1.221, Preprint
M. Oliver and S. Shkoller (2001). The vortex blob method as a second-grade non-Newtonian fluid. Comm. Partial Differential Equations 26, 295–314. DOI: 10.1081/PDE-100001756, Preprint
M. Oliver and E. S. Titi (2001). On the domain of analyticity of solutions of second order analytic nonlinear differential equations. J. Differential Equations 174, 55–74. DOI: 10.1006/jdeq.2000.3927, Preprint
S. Kouranbaeva and M. Oliver (2000). Global well-posedness for the averaged Euler equations in two dimensions. Phys. D 138, 197–209. DOI: 10.1016/S0167-2789(99)00205-5, Preprint
S. J. A. Malham and M. Oliver (2000). Accelerating fronts in autocatalysis. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 456, 1609–1624. DOI: 10.1098/rspa.2000.0578, Preprint
M. Oliver and E. S. Titi (2000). Gevrey regularity for the attractor of a partially dissipative model of Bénard convection in a porous medium. J. Differential Equations 163, 292–311. DOI: 10.1006/jdeq.1999.3744, Preprint
M. Oliver and E. S. Titi (2000). Remark on the rate of decay of higher order derivatives for solutions to the Navier–Stokes equations in ℝn. J. Funct. Anal. 172, 1–18. DOI: 10.1006/jfan.1999.3550, Preprint
M. Oliver and E. S. Titi (1998). Analyticity of the attractor and the number of determining nodes for a weakly damped driven nonlinear Schrödinger equation. Indiana Univ. Math. J. 47, 49–73. DOI: 10.1512/iumj.1998.47.1465, Preprint
C. D. Levermore and M. Oliver (1997). Analyticity of solutions for a generalized Euler equation. J. Differential Equations 133, 321–339. DOI: 10.1006/jdeq.1996.3200, Preprint
C. D. Levermore and M. Oliver (1997). Distribution-valued initial data for the complex Ginzburg–Landau equation. Comm. Partial Differential Equations 22, 39–48. DOI: 10.1080/03605309708821254, Preprint
M. Oliver (1997). Classical solutions for a generalized Euler equation in two dimensions. J. Math. Anal. Appl. 215, 471–484. DOI: 10.1006/jmaa.1997.5647, Preprint
M. Oliver (1997). Justification of the shallow water limit for a rigid lid flow with bottom topography. Theor. Comput. Fluid Dyn. 9, 311–324. DOI: 10.1007/s001620050047, Preprint
M. V. Bartuccelli, J. D. Gibbon, and M. Oliver (1996). Length scales in solutions of the complex Ginzburg–Landau equation. Phys. D 89, 267–286. DOI: 10.1016/0167-2789(95)00275-8, Preprint
C. D. Levermore, M. Oliver, and E. S. Titi (1996). Global well-posedness for models of shallow water in a basin with a varying bottom. Indiana Univ. Math. J. 45, 479–510. DOI: 10.1512/iumj.1996.45.1199, Preprint
C. D. Levermore, M. Oliver, and E. S. Titi (1996). Global well-posedness for the lake equations. Phys. D 98, 492–509. DOI: 10.1016/0167-2789(96)00108-X, Preprint
S. Danilov, S. Juricke, A. Kutsenko, and M. Oliver (2019). Toward consistent subgrid momentum closures in ocean models. In Energy transfers in atmosphere and ocean (Vol. 1, pp. 145–192). Springer, Cham. DOI: 10.1007/978-3-030-05704-6_5, Preprint
C. L. E. Franzke, M. Oliver, J. D. M. Rademacher, and G. Badin (2019). Multi-scale methods for geophysical flows. In Energy transfers in atmosphere and ocean (Vol. 1, pp. 1–51). Springer, Cham. DOI: 10.1007/978-3-030-05704-6_1, Preprint
J.-S. von Storch, G. Badin, and M. Oliver (2019). The interior energy pathway: Inertia-gravity wave emission by oceanic flows. In Energy transfers in atmosphere and ocean (Vol. 1, pp. 53–85). Springer, Cham. DOI: 10.1007/978-3-030-05704-6_2, Preprint
R. M. Kerr and M. Oliver (2013). Regulär oder nicht regulär? Strömungssingularitäten auf der spur. In D. Schleicher & M. Lackmann (Eds.), Eine einladung in die mathematik (pp. 141–170). Springer Spektrum. DOI: 10.1007/978-3-642-25798-8_10, Preprint
R. M. Kerr and M. Oliver (2011). The ever-elusive blowup in the mathematical description of fluids. In D. Schleicher & M. Lackmann (Eds.), An invitation to mathematics: From competitions to research (pp. 137–164). Springer-Verlag. DOI: 10.1007/978-3-642-19533-4_10, Preprint
C. D. Levermore and M. Oliver (1996). The complex Ginzburg–Landau equation as a model problem. In Dynamical systems and probabilistic methods in partial differential equations (Berkeley, CA, 1994) (Vol. 31, pp. 141–190). Amer. Math. Soc., Providence, RI. Preprint
G. Badin, J. Behrens, C. Franzke, M. Oliver, and J. Rademacher (2019). Introduction [Mathematical developments in geophysical fluid dynamics: Structure, vortices, and waves]. Geophys. Astrophys. Fluid Dyn. 113, 425–427. DOI: 10.1080/03091929.2019.1655259
M. Oliver (2008). Book review, “Musimathics” by G. Loy, Vol. 1 & 2. J. Math. Psychol. 52, 265–267. DOI: 10.1016/j.jmp.2008.05.005
V. Molchanov and M. Oliver (2008). Convergence of the Hamiltonian particle-mesh method applied to barotropic fluid equations. Proc. Appl. Math. Mech. 8, 10127–10128. DOI: 10.1002/pamm.200810127
M. Oliver and O. Bühler (2008). Transparent boundary conditions as dissipative closures. Proc. Appl. Math. Mech. 8, 10601–10602. DOI: 10.1002/pamm.200810601
M. Oliver (1997). Shallow water models: Well-posedness, regularity, and justification. Proceedings of the 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics 3, 295–300.
M. Oliver (1996). A mathematical investigation of models of shallow water with a varying bottom [PhD thesis]. The University of Arizona.
M. Oliver (1992). Attractors, regularity and length scales in the complex Ginzburg–Landau equation with a nonlinearity of arbitrary order [Master’s thesis]. WWU Münster; Imperial College, London.