On Entropy Solutions of Scalar Conservation Laws with Discontinuous FluxArchive for Rational Mechanics and Analysis - Tập 247 - Trang 1-40 - 2023
Evgeny Yu. Panov
We introduce the notion of entropy solutions (e.s.) to a conservation law with an arbitrary jump continuous flux vector and prove the existence of the largest and the smallest e.s. to the Cauchy problem. The monotonicity and stability properties of these solutions are also established. In the case of a periodic initial function, we derive the uniqueness of e.s. Generally, the uniqueness property c...... hiện toàn bộ
Directional Oscillations, Concentrations, and Compensated Compactness via Microlocal Compactness FormsArchive for Rational Mechanics and Analysis - Tập 215 - Trang 1-63 - 2014
Filip Rindler
This work introduces microlocal compactness forms (MCFs) as a new tool to study oscillations and concentrations in L
p
-bounded sequences of functions. Decisively, MCFs retain information about the location, value distribution, and direction of oscillations and concentrations, thus extending at the same time the theories of (generalized) Young measures and H-measu...... hiện toàn bộ
On the Structure of $${L^\infty}$$ -Entropy Solutions to Scalar Conservation Laws in One-Space DimensionArchive for Rational Mechanics and Analysis - Tập 226 - Trang 441-493 - 2017
S. Bianchini, E. Marconi
We prove that if u is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics. In particular, the characteristic curves are segments outside a countably 1-rectifiable set and the left and right trace...... hiện toàn bộ
Linear Vortex Symmetrization: The Spectral Density FunctionArchive for Rational Mechanics and Analysis - Tập 246 - Trang 61-137 - 2022
Alexandru D. Ionescu, Hao Jia
We investigate solutions of the 2d incompressible Euler equations, linearized around steady states which are radially decreasing vortices. Our main goal is to understand the smoothness of what we call the spectral density function associated with the linearized operator, which we hope will be a step towards proving full nonlinear asymptotic stability of radially decreasing vortices. The motivation...... hiện toàn bộ