Well-posedness of the free boundary problem in compressible elastodynamics

DOI10.1016/j.jde.2017.10.005zbMath1432.76211arXiv1705.11120OpenAlexW2962889108MaRDI QIDQ1678235

Yu. L. Trakhinin

Publication date: 14 November 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.11120

zbMATH Keywords

free boundary problemwell-posednessRayleigh-Taylor instabilitysymmetric hyperbolic systemcompressible elastodynamics

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial-boundary value problems for first-order hyperbolic systems (35L50) Free boundary problems for PDEs (35R35) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)

Related Items (19)

Incompressible limit of nonisentropic Hookean elastodynamics ⋮ Local well-posedness and incompressible limit of the free-boundary problem in compressible elastodynamics ⋮ Local well-posedness of free-boundary incompressible elastodynamics with surface tension via vanishing viscosity limit ⋮ Low Mach number limit of inviscid Hookean elastodynamics ⋮ Nonlinear stability and existence of compressible vortex sheets in 2D elastodynamics ⋮ Stability of multidimensional thermoelastic contact discontinuities ⋮ On the vortex sheets of compressible flows ⋮ Local well-posedness of the plasma-vacuum interface problem for the ideal incompressible MHD ⋮ Vanishing viscosity limits for the free boundary problem of compressible viscoelastic fluids with surface tension ⋮ Low Mach number limit of nonisentropic inviscid Hookean elastodynamics ⋮ Stabilization effect of elasticity on three-dimensional compressible vortex sheets ⋮ Structural stability of shock waves in 2D compressible elastodynamics ⋮ Well-posedness of the free boundary problem for incompressible elastodynamics ⋮ Well-Posedness of the Free Boundary Problem in Elastodynamics with Mixed Stability Condition ⋮ Well-posedness of the free boundary problem in incompressible elastodynamics under the mixed type stability condition ⋮ Incompressible limit of the Hookean elastodynamics in a bounded domain ⋮ Structural stability of shock waves and current-vortex sheets in shallow water magnetohydrodynamics ⋮ Convergence rates of solutions to the compressible Hookean elastodynamics ⋮ On the stability of two-dimensional nonisentropic elastic vortex sheets

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