107 citations · 1.1k across the 120 of their papers we have counts for
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Hopf bifurcation of viscous shock wave solutions of compressible Navier-Stokes equations and MHD
Benjamin Texier, Kevin Zumbrun
Extending our previous results for artificial viscosity systems, we show, under suitable spectral hypotheses, that shock wave solutions of compressible Navier--Stokes (cNS) and mag…
Galloping instability of viscous shock waves
Benjamin Texier, Kevin Zumbrun
Motivated by physical and numerical observations of time oscillatory ``galloping'', ``spinning'', and ``cellular'' instabilities of detonation waves, we study Poincaré--Hopf bifurc…
Nonclassical multidimensional viscous and inviscid shocks
Olivier Gues, Guy Métivier, Mark Williams +1
Extending our earlier work on Lax-type shocks of systems of conservation laws, we establish existence and stability of curved multidimensional shock fronts in the vanishing viscosi…
Pointwise Green function bounds and stability of combustion waves
Gregory Lyng, Mohammadreza Raoofi, Benjamin Texier +1
Generalizing similar results for viscous shock and relaxation waves, we establish sharp pointwise Green function bounds and linearized and nonlinear stability for traveling wave so…
Viscous Boundary Value Problems for Symmetric Systems with Variable Multiplicities
Olivier Gues, Guy Métivier, Mark Williams +1
Extending investigations of Métivier&Zumbrun in the hyperbolic case, we treat stability of viscous shock and boundary layers for viscous perturbations of multidimensional hyperboli…
A sharp stability criterion for propagating phase boundaries in Korteweg's model
K. Zumbrun
Recently, Benzoni--Gavage, Danchin, Descombes, and Jamet have given a sufficient condition for linear and nonlinear stability of solitary wave solutions of Korteweg's model for pha…