For fractional Laplacian order 1 < alpha < 2, solutions of the scaled fractal Burgers equation converge in L^2 to the entropy shock, with a shift and a convergence rate that tends to zero.
Contraction property for large perturbations of shocks of the barotropic Navier-Stokes system
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
This paper is dedicated to the construction of a pseudo-norm, for which small shock profiles of the barotropic Navier-Stokes equation have a contraction property. This contraction property holds in the class of any large 1D weak solutions to the barotropic Navier-Stokes equation. It implies a stability condition which is independent of the strength of the viscosity. The proof is based on the relative entropy method, and is reminiscent to the notion of a-contraction first introduced by the authors in the hyperbolic case.
fields
math.AP 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Inviscid limit to the shock waves for the fractal Burgers equation
For fractional Laplacian order 1 < alpha < 2, solutions of the scaled fractal Burgers equation converge in L^2 to the entropy shock, with a shift and a convergence rate that tends to zero.