A new convex integration approach for the compressible Euler equations and failure of the local maximal dissipation criterion

DOI10.1088/1361-6544/AD81C8MaRDI QIDQ6633346

Simon Markfelder

Publication date: 5 November 2024

Published in: Nonlinearity (Search for Journal in Brave)

zbMATH Keywords

weak solutionsnon-uniquenesscompressible Euler equationsbarotropic Euler equationsconvex integrationentropy rate admissibility criterionmaximal dissipation criterion

Mathematics Subject Classification ID

Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Systems of nonlinear first-order PDEs (35F50)

Cites Work

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• On the energy dissipation rate of solutions to the compressible isentropic Euler system
• On admissibility criteria for weak solutions of the Euler equations
• The Euler equations as a differential inclusion
• The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock
• Maximal dissipation and well-posedness for the compressible Euler system
• The entropy rate admissibility criterion for solutions of hyperbolic conservation laws
• A counterexample to well-posedness of entropy solutions to the compressible Euler system
• Partial Differential Relations
• On contact discontinuities in multi-dimensional isentropic Euler equations
• Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations
• Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations
• On Bounded Two-Dimensional Globally Dissipative Euler Flows
• NonUnique Admissible Weak Solutions of the Compressible Euler Equations with Compact Support in Space
• Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations
• Global Ill‐Posedness of the Isentropic System of Gas Dynamics
• Weak Solutions to Problems Involving Inviscid Fluids
• Non–uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data
• Topology
• A general convex integration scheme for the isentropic compressible Euler equations

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