Stability of a supersonic flow past a wedge with adjoint weak neutrally stable shock wave

A. M. Blokhin, D. L. Tkachev

Research output: Contribution to journalArticlepeer-review

Abstract

We study the classical problem of a supersonic stationary flow of a nonviscous nonheat-conducting gas in local thermodynamic equilibrium past an infinite plane wedge. Under the Lopatinskiĭ condition on the shock wave (neutral stability), we prove the well-posedness of the linearized mixed problem (the main solution is a weak shock wave), obtain a representation of the classical solution, where, in this case (in contrast to the case of the uniform Lopatinskiĭ condition—an absolutely stable shock wave), plane waves additionally appear in the representation. If the initial data have compact support, the solution reaches the given regime in infinite time.

Original languageEnglish
Pages (from-to)77-102
Number of pages26
JournalSiberian Advances in Mathematics
Volume27
Issue number2
DOIs
Publication statusPublished - 1 Apr 2017

Keywords

  • (Lyapunov) asymptotic stability
  • Lopatinskiĭ condition
  • weak shock wave

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