Non-linear asymptotic stability for the through-passing flows of inviscid incompressible fluid

Article type: Research Article

Authors: Morgulis, A.

Affiliations: Department of Mathematics, Mechanics and Computer Science, The South Federal University, Rostov-na-Donu and South Institute of Mathematics, Vladikavkaz Scientific Center RAS, Vladikavkaz, Russia. E-mail: amor@math.rsu.ru

Note: [] Present address: 8a, Milchakova str., Rostov-na-Donu, 344090, Russia.

Abstract: The paper addresses the dynamics of inviscid incompressible fluid confined within bounded domain with the inflow and outflow of fluid through certain parts of the boundary. This system is non-conservative essentially since the fluxes of energy and vorticity through the flow boundary are not equal to zero. Therefore, the dynamics of such flows should demonstrate the generic non-conservative phenomena such as the asymptotic stability of the equilibria, the onset of instability or the excitation of the self-oscillations, etc. These phenomena are studied extensively for the flows of the viscous fluids but not for the inviscid ones. In this paper, we prove a sufficient condition for the non-linear asymptotic stability of the inviscid steady flows.

Keywords: asymptotic stability, inviscid fluid, Euler equations

DOI: 10.3233/ASY-2009-0968

Journal: Asymptotic Analysis, vol. 66, no. 3-4, pp. 229-247, 2010