This article is cited in 1 paper

On the blow-up of internal gravitational waves with non-linear sources

M. O. Korpusov

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: We consider an equation of internal gravitational waves in a stratified fluid in which non-linear sources of a general form are taken into account. In the case of the corresponding initial-boundary-value problem in a bounded domain with homogeneous Dirichlet conditions on the boundary, we prove the local-in-time solubility and also obtain sufficient conditions for the blow-up of a solution in finite time.

Keywords: blow-up, non-linear initial-boundary-value problem, internal waves, equation of Sobolev type.

UDC: 517.957

MSC: Primary 76B15; Secondary 35Q75

Received: 16.12.2009

DOI: 10.4213/im4277

 English version: Izvestiya: Mathematics, 2011, 75:4, 691–710

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