10 papers · 1 filter
The computational ansatz for convex integration of hyperbolic systems and a resolution of the Strong Trace Conjecture
Sam G. Krupa
In this paper, we consider hyperbolic systems of conservation laws in one spatial dimension. We use the computational ansatz introduced in the hyperbolic theory by the a…
The unique limit of the Glimm-Lax construction for Sobolev data and obstructions to 1-d convex integration
Jeffrey Cheng, Cooper Faile, Sam G. Krupa
We consider a genuinely nonlinear -d system of hyperbolic conservation laws with two unknowns. A famous construction of Glimm & Lax shows that global-in-time "Glimm-Lax" weak en…
Quantitative weak-BV stability of "wild'' solutions to compressible Euler equations, with a view towards higher systems
Geng Chen, Cooper Faile, Sam G. Krupa
For hyperbolic systems of conservation laws, including important physical models from continuum mechanics, the question of stability for large data solutions remains a challenging…
Solutions to conservation laws are Hölder-stable in in the weak-BV setting
Geng Chen, Cooper Faile, Sam G. Krupa
We consider hyperbolic systems of conservation laws in one spatial dimension. For any limit of front tracking solutions , and for a general weak solution with no…
Contact discontinuities for 2-D isentropic Euler are unique in 1-D but wildly non-unique otherwise
Sam G. Krupa, László Székelyhidi
We develop a general framework for studying non-uniqueness of the Riemann problem for the isentropic compressible Euler system in two spatial dimensions, and in this paper we prese…
Finite time BV blowup for Liu-admissible solutions to -system via computer-assisted proof
Sam G. Krupa
In this paper, we consider finite time blowup of the -norm for exact solutions to genuinely nonlinear hyperbolic systems in one space dimension, in particular the -system. W…