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Metastability and rapid convergence to quasi-stationary bar states for the two-dimensional Navier–Stokes equations

Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 2013-10, Vol.143 (5), p.905-927

2013

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A biologically constrained, mathematical model of cortical wave propagation preceding seizure termination

PLoS computational biology, 2015-02, Vol.11 (2), p.e1004065-e1004065

2015

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Using Global Invariant Manifolds to Understand Metastability in the Burgers Equation with Small Viscosity

SIAM review, 2011-01, Vol.53 (1), p.129-153

2011

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Decay of Hamiltonian Breathers Under Dissipation

Communications in mathematical physics, 2020-11, Vol.380 (1), p.71-102

2020

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Rigorous Justification of Taylor Dispersion via Center Manifolds and Hypocoercivity

Archive for rational mechanics and analysis, 2020-02, Vol.235 (2), p.1105-1149

2020

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Vortices in stably-stratified rapidly rotating Boussinesq convection

Nonlinearity, 2019-05, Vol.32 (5), p.R1-R52

2019

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Dynamics of Partial Differential Equations

1st ed. 2015, 2015

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The rigorous approximation of long-wavelength capillary-gravity waves

Archive for rational mechanics and analysis, 2002-04, Vol.162 (3), p.247-285

2002

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Energy dissipation in Hamiltonian chains of rotators

Nonlinearity, 2017-11, Vol.30 (11), p.R81-R117

2017

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Breathers as metastable states for the discrete NLS equation

Discrete and continuous dynamical systems. Series A, 2018-12, Vol.38 (12), p.6091-6103

2018

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Global stability of vortex solutions of the two-dimensional Navier-Stokes equation

Communications in mathematical physics, 2005-04, Vol.255 (1), p.97-129

2005

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Modified energy functionals and the NLS approximation

Discrete and continuous dynamical systems. Series A, 2017-03, Vol.37 (3), p.1295-1321

2017

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Justification of the NLS approximation for a quasilinear water wave model

Journal of Differential Equations, 2011-07, Vol.251 (2), p.238-269

2011

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Justification of the Nonlinear Schrödinger Equation for the Evolution of Gravity Driven 2D Surface Water Waves in a Canal of Finite Depth

Archive for rational mechanics and analysis, 2016-05, Vol.220 (2), p.543-602

2016

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A multi-moment vortex method for 2D viscous fluids

Journal of computational physics, 2012-02, Vol.231 (4), p.1705-1727

2012

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Invariant Manifolds and the Long-Time Asymptotics of the Navier-Stokes and Vorticity Equations on R 2

Archive for rational mechanics and analysis, 2002-06, Vol.163 (3), p.209-258

2002

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The long-wave limit for the water wave problem I. The case of zero surface tension

Communications on pure and applied mathematics, 2000-12, Vol.53 (12), p.1475-1535

2000

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Long-time approximations of small-amplitude, long-wavelength FPUT solutions

Discrete and continuous dynamical systems. Series A, 2024-04, Vol.44 (4), p.905-928

2024

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Long-time asymptotics of the Navier-Stokes and vorticity equations on R(3)

Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences, 2002-10, Vol.360 (1799), p.2155-2188

2002

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Newton's method and periodic solutions of nonlinear wave equations

Communications on pure and applied mathematics, 1993-12, Vol.46 (11), p.1409-1498

1993

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Asymptotic approximation of a modified compressible Navier-Stokes system

Indiana University mathematics journal, 2023, Vol.72 (3), p.1175-1237

2023

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Critical Points of Strichartz Functional

Experimental mathematics, 2021-04, Vol.30 (2), p.235-257

2021

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Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory

Communications in mathematical physics, 1990-02, Vol.127 (3), p.479-528

WAYNE, C. E

1990

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Existence and Stability of Asymmetric Burgers Vortices

Journal of mathematical fluid mechanics, 2007-06, Vol.9 (2), p.243-261

2007

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Analysis of Enhanced Diffusion in Taylor Dispersion via a Model Problem

Hamiltonian Partial Differential Equations and Applications, 2015, Vol.75, p.31-71

2015

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Metastability and rapid convergence to quasi-stationary bar states for the two-dimensional Navier–Stokes equations

A biologically constrained, mathematical model of cortical wave propagation preceding seizure termination

Using Global Invariant Manifolds to Understand Metastability in the Burgers Equation with Small Viscosity

Decay of Hamiltonian Breathers Under Dissipation

Rigorous Justification of Taylor Dispersion via Center Manifolds and Hypocoercivity

Vortices in stably-stratified rapidly rotating Boussinesq convection

Dynamics of Partial Differential Equations

The rigorous approximation of long-wavelength capillary-gravity waves

Energy dissipation in Hamiltonian chains of rotators

Breathers as metastable states for the discrete NLS equation

Global stability of vortex solutions of the two-dimensional Navier-Stokes equation

Modified energy functionals and the NLS approximation

Justification of the NLS approximation for a quasilinear water wave model

Justification of the Nonlinear Schrödinger Equation for the Evolution of Gravity Driven 2D Surface Water Waves in a Canal of Finite Depth

A multi-moment vortex method for 2D viscous fluids

Invariant Manifolds and the Long-Time Asymptotics of the Navier-Stokes and Vorticity Equations on R 2

The long-wave limit for the water wave problem I. The case of zero surface tension

Long-time approximations of small-amplitude, long-wavelength FPUT solutions

Long-time asymptotics of the Navier-Stokes and vorticity equations on R(3)

Newton's method and periodic solutions of nonlinear wave equations

Asymptotic approximation of a modified compressible Navier-Stokes system

Critical Points of Strichartz Functional

Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory

Existence and Stability of Asymmetric Burgers Vortices

Analysis of Enhanced Diffusion in Taylor Dispersion via a Model Problem

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