Publications


Preprints:

G.A. Gottwald, H. Mohamad, and M. Oliver,
Optimal balance via adiabatic invariance of approximate slow manifolds,
submitted for publication.

C.L.E. Franzke, M. Oliver, J.D.M. Rademacher, and G. Badin
Multi-scale methods for geophysical flows,
submitted for publication.

J.-S. von Storch, G. Badin, and M. Oliver
The interior energy pathway: inertial gravity wave emission by oceanic flows,
submitted for publication.

M. Oliver,
Lagrangian averaging with geodesic mean,
submitted for publication.

M. Oliver and S. Vasylkevych,
A new construction of modified equations for variational integrators,
submitted for publication.

M. Oliver and S. Vasylkevych,
Non-negative matrix factorization with factorizable feature matrix,
submitted for publication.


Refereed Articles:

D.G. Dritschel, G.A. Gottwald, and M. Oliver,
Comparison of variational balance models for the rotating shallow water equations,
J. Fluid Mech., to appear.

C. Wulff and M. Oliver,
Exponentially accurate Hamiltonian embeddings of symplectic A-stable Runge-Kutta methods for Hamiltonian semilinear evolution equations,
P. Roy. Soc. Edinb. 146A (2016), 1265-1301.

M. Oliver and S. Vasylkevych,
Generalized large-scale semigeostrophic approximations for the f-plane primitive equations,
J. Phys. A: Math. Theor. 49 (2016), 184001.

A. Merico, G. Brandt, S.L. Smith, and M. Oliver,
Sustaining diversity in trait-based models of phytoplankton communities,
Front. Ecol. Evol. 2 (2014), 59, doi:10.3389/fevo.2014.00059.

G. Gottwald and M. Oliver,
Slow dynamics via degenerate variational asymptotics,
Proc. R. Soc. Lond. A 470 (2014), 20140460, doi:10.1098/rspa.2014.0460.

M. Oliver,
A variational derivation of the geostrophic momentum approximation,
J. Fluid Mech. 751 (2014), R2, doi:10.1017/jfm.2014.309.

M. Oliver and C. Wulff,
Stability under Galerkin truncation of A-stable Runge-Kutta discretizations in time,
P. Roy. Soc. Edinb. A 144 (2014), 603-636.

O. Bokhove, V. Molchanov, M. Oliver, and B. Peeters,
On the rate of convergence of the Hamiltonian particle-mesh method,
in: Meshfree Methods for Partial Differential Equations VI (M. Griebel and M.A. Schweitzer, eds.), Lecture Notes in Computational Science and Engineering Vol. 89, Springer, Berlin, 2013, pp. 25-43.

M. Çalık, M. Oliver, and S. Vasylkevych,
Global well-posedness for the generalized large-scale semigeostrophic equations,
Arch. Ration. Mech. An. 207 (2013), 969-990.

M. Çalık and M. Oliver,
Weak solutions for generalized large-scale semigeostrophic equations,
Commun. Pure Appl. Ana. 12 (2013), 939-955.

V. Molchanov and M. Oliver,
Convergence of the Hamiltonian particle-mesh method for barotropic fluid flow,
Math. Comp. 82 (2013), 861-891.

M. Oliver and S. Vasylkevych,
Generalized LSG models with varying Coriolis parameter,
Geophys. Astrophys. Fluid Dyn. 107 (2013), 259-276.

M. Oliver and C. Wulff,
A-stable Runge-Kutta methods for semilinear evolution equations,
J. Functional Anal. 263 (2012), 1981-2023.

M. Oliver and S. Vasylkevych,
Hamiltonian formalism for models of rotating shallow water in semigeostrophic scaling,
Discret. Contin. Dyn. S. 31 (2011), 827-846.

G. Gottwald and M. Oliver,
Boltzmann's dilemma: an introduction to statistical mechanics via the Kac ring,
SIAM Rev. 51 (2009), 613-635.

O. Bokhove and M. Oliver,
A parcel formulation for Hamiltonian layer models,
Geophys. Astrophys. Fluid Dyn. 103 (2009), 423-442.

M. Oliver and O. Bühler,
Transparent boundary conditions as dissipative subgrid closures for the spectral representation of scalar advection by shear flows,
J. Math. Phys. 48 (2007), 065502, 26 pp.

G. Gottwald, M. Oliver, and N. Tecu,
Long-time accuracy for approximate slow manifolds in a finite dimensional model of balance,
J. Nonlinear Sci. 17 (2007), 283-307.

O. Bokhove and M. Oliver,
Parcel Eulerian-Lagrangian fluid dynamics of rotating geophysical flows,
Proc. R. Soc. Lond. A 462 (2006), 2563-2573.

M. Oliver,
Variational asymptotics for rotating shallow water near geostrophy: A transformational approach,
J. Fluid Mech. 551 (2006), 197-234.

N.D. Aparicio, S.J.A. Malham, and M. Oliver,
Numerical evaluation of the Evans function by Magnus integration,
BIT Numerical Mathematics 45 (2005), 219-258.

M. Oliver, M. West, and C. Wulff,
Approximate momentum conservation for spatial semidiscretizations of nonlinear wave equations,
Numerische Mathematik 97 (2004), 493-535.

R. Ford, S.J.A. Malham, and M. Oliver,
A new model for shallow water in the low Rossby-number limit,
J. Fluid Mech. 450 (2002), 287-296.

M. Oliver,
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. Ana. 1 (2002), 221-235.

M. Oliver and E.S. Titi,
On the domain of analyticity for solutions of second order analytic nonlinear differential equations,
J. Differential Equations 174 (2001), 55-74.

M. Oliver and S. Shkoller,
The vortex blob method as a second-grade non-Newtonian fluid,
Comm. Partial Differential Equations 26 (2001), 295-314.

M. Oliver and S. Malham,
Accelerating fronts in autocatalysis,
Proc. R. Soc. Lond. A 456 (2000), 1609-1624.

M. Oliver and E.S. Titi,
Gevrey regularity for the attractor of a partially dissipative model of Bénard convection in a porous medium,
J. Differential Equations 163 (2000), 292-311.

S. Kouranbaeva and M. Oliver,
Global Well-Posedness for the Averaged Euler Equations in Two Dimensions,
Phys. D 138 (2000), 197-209.

M. Oliver and E.S. Titi,
Remark on the rate of decay of higher order derivatives for solutions to the Navier-Stokes equations in Rn,
J. Funct. Anal. 172 (2000), 1-18.

M. Oliver and E.S. Titi,
Analyticity of the attractor and the number of determining nodes for a weakly damped driven nonlinear Schrödinger Equation,
Indiana Univ. Math. J. 47 (1998), 49-74.

M. Oliver,
Justification of the shallow water limit for a rigid lid flow with bottom topography,
Theoretical and Computational Fluid Dynamics 9 (1997), 311-324.

M. Oliver,
Classical solutions for a generalized Euler equation in two dimensions,
J. Math. Anal. Appl. 215 (1997), 471-484.

C.D. Levermore and M. Oliver,
Analyticity of solutions for a generalized Euler equation,
J. Differential Equations 133 (1997), 321-339.

C.D. Levermore and M. Oliver,
Distribution-valued initial data for the complex Ginzburg-Landau equation,
Comm. Partial Differential Equations 22 (1997), 39-48.

C.D. Levermore, M. Oliver, and E.S. Titi,
Global well-posedness for models of shallow water in a basin with a varying bottom,
Indiana Univ. Math. J. 45 (1996), 479-510.

C.D. Levermore, M. Oliver, and E.S. Titi,
Global Well-Posedness for the Lake Equations,
Physica D 98 (1996), 492-509.

M. Bartuccelli, J.D. Gibbon, and M. Oliver,
Length scales in solutions of the complex Ginzburg-Landau equation,
Physica D 89 (1996), 267-286.


Invited Review Articles:

R.M. Kerr and M. Oliver,
The ever-elusive blowup in the mathematical description of fluids,
in: "An Invitation to Mathematics: From Competitions to Research," D. Schleicher and M. Lackmann (eds.), pp. 137-164, Springer-Verlag, Berlin, 2011.
Also published in German as: Regulär oder nicht regulär? Strömungssingularitäten auf der Spur,
in: "Eine Einladung in die Mathematik," D. Schleicher and M. Lackmann (eds.), pp. 141-170, Springer-Verlag, Berlin, 2013.

C.D. Levermore and M. Oliver,
The complex Ginzburg-Landau equation as a model problem,
in "Lectures in Applied Mathematics," Vol. 31, pp. 141-190, AMS, Providence, Rhode Island, 1996.


Other Publications:

M. Oliver,
Shallow Water Models: Well-posedness, Regularity, and Justification,
in ``Proceedings of the 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, Berlin, August 1997,'' Vol. 3, pp. 295-300, Verlag Wissenschaft & Technik, Berlin, 1997.

M. Oliver,
A Mathematical Investigation of Models of Shallow Water with a Varying Bottom,
Ph.D. dissertation, University of Arizona, Tucson, Arizona, 1996.

M. Oliver,
Attractors, Regularity and Length Scales in the Complex Ginzburg-Landau Equation with a Nonlinearity of Arbitrary Order,
Diplomarbeit, WWU Münster and Imperial College, London, 1992.




Last modified: 2017/05/05
Marcel Oliver (oliver@member.ams.org)