Nonuniform Dependence on Initial Data for Compressible Gas Dynamics: The Cauchy Problem on $\mathbb{R}^2$

DOI10.1137/16M1103968zbMath1391.35263arXiv1611.05894OpenAlexW2557124825MaRDI QIDQ4603746

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Publication date: 19 February 2018

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.05894

zbMATH Keywords

Sobolev spacesCauchy problemEuler equationconservation lawnonlinear PDEcompressible gastwo-dimensional compressible Euler equationslow- and high-frequency approximations

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial value problems for first-order hyperbolic systems (35L45) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Euler equations (35Q31)

Related Items (7)

Non-uniform dependence on initial data for the Benjamin-Ono equation ⋮ Nonuniform dependence on initial data for compressible gas dynamics: the periodic Cauchy problem ⋮ Non-uniform dependence of the data-to-solution map for the two-component Fornberg-Whitham system ⋮ Nonuniform dependence on initial data for the 2D viscous shallow water equations ⋮ Hyperbolic Conservation Laws and L2 ⋮ Non-uniform dependence for Euler equations in Besov spaces ⋮ Continuity properties of the solution map for the Euler-Poisson equation

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