JournalsaihpcVol. 14, No. 2pp. 187–209

Nonlinear instability in an ideal fluid

  • Misha Vishik

    Department of Mathematics, University of Texas at Austin, Austin, TX 78712 USA

  • Susan Friedlander

    Department of Mathematics, University of Illinois at Chicago, Chicago, IL 60680 USA

  • Walter Strauss

    Department of Mathematics, Brown University, Providence, RI 02912 USA
Nonlinear instability in an ideal fluid cover
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Abstract

Linearized instability implies nonlinear instability under certain rather general conditions. This abstract theorem is applied to the Euler equations governing the motion of an inviscid fluid. In particular this theorem applies to all space periodic flows without stagnation points as well as space-periodic shear flows.

Résumé

L’instabilité linéarisée implique l’instabilité non linéaire sous certaines conditions assez générales. Ce théorème abstrait s’applique aux équations d’Euler qui gouvernent le mouvement d’un fluide non visqueux. En particulier ce théorème s’applique à tous les flots périodiques dans le plan, soit sans point de stagnation, soit des écoulements de cisaillement.

Cite this article

Misha Vishik, Susan Friedlander, Walter Strauss, Nonlinear instability in an ideal fluid. Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997), no. 2, pp. 187–209

DOI 10.1016/S0294-1449(97)80144-8