Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations

Daniel Han-Kwan, Toan T. Nguyen

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

In this paper, we develop an abstract framework to establish ill-posedness, in the sense of Hadamard, for some nonlocal PDEs displaying unbounded unstable spectra. We apply this to prove the ill-posedness for the hydrostatic Euler equations as well as for the kinetic incompressible Euler equations and the Vlasov–Dirac–Benney system.

Original languageEnglish (US)
Pages (from-to)1317-1344
Number of pages28
JournalArchive for Rational Mechanics and Analysis
Volume221
Issue number3
DOIs
StatePublished - Sep 1 2016

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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