107 citations · 1.1k across the 120 of their papers we have counts for
15 papers · 1 filter
Existence and stability of viscous shock profiles for 2-D isentropic MHD with infinite electrical resistivity
Blake Barker, Olivier Lafitte, Kevin Zumbrun
For the two-dimensional Navier--Stokes equations of isentropic magnetohydrodynamics (MHD) with -law gas equation of state, , and infinite electrical resistivity, we carr…
Rigorous Justification of the Whitham Modulation Equations for the Generalized Korteweg-de Vries Equation
Mathew Johnson, Kevin Zumbrun
In this paper, we consider the spectral stability of spatially periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long-wavelength perturbations. Spe…
Instantaneous shock location and one-dimensional nonlinear stability of viscous shock wave
Kevin Zumbrun
We illustrate in a simple setting the instantaneous shock tracking approach to stability of viscous conservation laws introduced by Howard, Mascia, and Zumbrun. This involves a cho…
Transverse Instability of Periodic Traveling Waves in the Generalized Kadomtsev-Petviashvili Equation
Mathew A. Johnson, Kevin Zumbrun
In this paper, we investigate the spectral instability of periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transverse perturbation…
Existence of quasilinear relaxation shock profiles
Guy Metivier, Benjamin Texier, Kevin Zumbrun
We establish existence with sharp rates of decay and distance from the Chapman--Enskog approximation of small-amplitude quasilinear relaxation shocks in the general case that the p…
Stability of radiative shock profiles for hyperbolic-elliptic coupled systems
Toan Nguyen, Ramon Plaza, Kevin Zumbrun
Extending previous work with Lattanzio and Mascia on the scalar (in fluid-dynamical variables) Hamer model for a radiative gas, we show nonlinear orbital asymptotic stability of sm…