On the global existence and stability of a multi-dimensional supersonic conic shock wave

DOI10.1007/s00220-014-1974-4zbMath1298.35151arXiv1110.0626OpenAlexW2080128296MaRDI QIDQ2249760

Jun Li, Ingo Witt, Hui Cheng Yin

Publication date: 3 July 2014

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.0626

zbMATH Keywords

asymptotic behaviourweighted energy estimatesgloabl existence and stabilitymulti-dimensional supersonic conic shock wavesteady potential equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Supersonic flows (76J20)

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Cites Work

• Compressible fluid flow and systems of conservation laws in several space variables
• Global conic shock wave for the steady supersonic flow past a cone: isothermal case
• Global transonic conic shock wave for the symmetrically perturbed supersonic flow past a cone
• Formation of singularities in three-dimensional compressible fluids
• BV estimates fail for most quasilinear hyperbolic systems in dimensions greater than one
• Blowup of small data solutions for a quasilinear wave equation in two space dimensions.
• Lectures on nonlinear hyperbolic differential equations
• Systems of conservation laws. Two-dimensional Riemann problems
• Blowup of small data solutions for a class of quasilinear wave equations in two space dimensions. II
• Nonlinear stability of a self-similar 3-dimensional gas flow
• Global shock waves for the supersonic flow past a perturbed cone
• Global supersonic conic shock wave for the steady supersonic flow past a cone: Polytropic gas
• Global existence of null-form wave equations in exterior domains
• Global existence of a shock for the supersonic flow past a curved wedge
• The lifespan of a class of smooth spherically symmetric solutions of the compressible Euler equations with variable entropy in three space dimensions
• Supersonic flow past a symmetrically curved cone
• Instability of one global transonic shock wave for the steady supersonic Euler flow past a sharp cone
• Global solutions of nonlinear hyperbolic equations for small initial data
• Multi‐dimensional shock fronts for second order wave equations
• The existence of viscous profiles and admissibility for transonic shocks
• Global shock waves in some domains for the isentropic irrotational potential flow equations
• Almost global existence for quasilinear wave equations in three space dimensions
• Global Multidimensional Transonic Conic Shock Wave for the Perturbed Supersonic Flow Past a Cone
• GLOBAL MULTIDIMENSIONAL SHOCK WAVE FOR THE STEADY SUPERSONIC FLOW PAST A THREE-DIMENSIONAL CURVED CONE
• Long-Time Existence of Quasilinear Wave Equations Exterior to Star-Shaped Obstacles via Energy Methods
• THE LIFESPAN OF SOLUTIONS OF EXTERIOR RADIAL QUASILINEAR CAUCHY–NEUMANN PROBLEMS
• Similarity Laws of Hypersonic Flows
• Existence of stationary supersonic flows past a pointed body
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