Existence and Stability of Multidimensional Transonic Shocks for the Euler Equations for Steady Potential Fluids in Unbounded Domains

Gui-Qiang Chen () and Mikhail Feldman ()
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Gui-Qiang Chen: Northwestern University, Department of Mathematics
Mikhail Feldman: University of Wisconsin, Department of Mathematics

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 419-432 from Springer

Abstract: Abstract We are concerned with the existence and stability of multidimensional transonic shocks in inviscid compressible fluid dynamics. In this paper, we focus on inviscid steady potential fluid flows, which are governed by the Euler equations consisting of the conservation law of mass and the Bernoulli law for velocity. Then the Euler equations for the velocity potential ϕ: Ω ⊂ Rn → R can be formulated into the following second order nonlinear equation of mixed elliptic-hyperbolic type: (1) $$ div(\rho (|D\varphi {{|}^{2}})D\varphi ) = 0, $$ where the density function ρ(q 2) has the form: (2) $$ \rho ({{q}^{2}}) = {{\left( {1 - \frac{{\gamma - 1}}{2}{{q}^{2}}} \right)}^{{\frac{1}{{\gamma - 1}}}}} $$ with the adiabatic exponent ψ>1.

Keywords: Free Boundary; Unbounded Domain; Free Boundary Problem; Subsonic Flow; Infinite Cylinder (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_38

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DOI: 10.1007/978-3-642-55711-8_38

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