Space-time resonances and high-frequency Raman instabilities in the two-fluid Euler-Maxwell system

no code implementations • 17 Feb 2021 • Eric Dumas, Yong Lu, Benjamin Texier

A key step in the proof is the reformulation of the set of resonant frequencies as the locus of weak hyperbolicity for linearized equations around the WKB solution.

Analysis of PDEs

Dispersive regularization for phase transitions

no code implementations • 2 Feb 2021 • Federico Cacciafesta, Marta Strani, Benjamin Texier

We introduce a dispersive regularization of the compressible Euler equations in Lagrangian coordinates, in the one-dimensional torus.

Analysis of PDEs

On Métivier's Lax-Mizohata theorem and extensions to weak defects of hyperbolicity. Part one

no code implementations • 15 Dec 2020 • Karim Ndoumajoud, Benjamin Texier

We prove that, for first-order, fully nonlinear systems of partial differential equations, under an hypothesis of ellipticity for the principal symbol, the Cauchy problem has no solution within a range of Sobolev indices depending on the regularity of the initial datum.

Analysis of PDEs