Von Neumann’s comments about existence and uniqueness for the initial-boundary value problem in gas dynamics

DOI10.1090/S0273-0979-09-01286-5zbMath1179.01022OpenAlexW2143651450MaRDI QIDQ5850862

Denis Serre

Publication date: 20 January 2010

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-09-01286-5

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) PDEs in connection with fluid mechanics (35Q35) History of mathematics in the 20th century (01A60) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Gas dynamics (general theory) (76N15) Hyperbolic conservation laws (35L65) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Hydrodynamic and hydromagnetic problems in astronomy and astrophysics (85A30) PDEs in connection with astronomy and astrophysics (35Q85)

Related Items

Multidimensional transonic shock waves and free boundary problems, Well-posedness of Compressible Euler Equations in a Physical Vacuum, Approximate solutions to the initial value problem for some compressible flows, Free boundary problems in shock reflection/diffraction and related transonic flow problems, Supersonic flow onto solid wedges, multidimensional shock waves and free boundary problems, Stability of attached transonic shocks in steady potential flow past three-dimensional wedges, Prandtl-Meyer reflection for supersonic flow past a solid ramp, Well and ill-posedness for compressible Euler equations with vacuum, Stability of transonic shocks in steady supersonic flow past multidimensional wedges

Cites Work

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• Convergence of the viscosity method for isentropic gas dynamics
• BV estimates fail for most quasilinear hyperbolic systems in dimensions greater than one
• Hyperbolic systems of conservation laws II
• Potential theory for shock reflection by a large-angle wedge
• Solutions in the large for nonlinear hyperbolic systems of equations