Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations

Daniel Han-Kwan, Toan Nguyen

Research output: Contribution to journalArticle

5 Citations (Scopus)

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

Fingerprint

Vlasov equation
Vlasov Equation
Ill-posedness
Singular Equation
Hydrostatics
Euler equations
Euler
Incompressible Euler Equations
Euler Equations
Kinetics
Unstable
Framework

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

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Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations. / Han-Kwan, Daniel; Nguyen, Toan.

In: Archive for Rational Mechanics and Analysis, Vol. 221, No. 3, 01.09.2016, p. 1317-1344.

Research output: Contribution to journalArticle

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