Geodesic
On the blow-up of internal gravitational waves with non-linear sources
Izvestiya. Mathematics , Tome 75 (2011) no. 4, pp. 691-710

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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. 
@article{IM2_2011_75_4_a2,
     author = {M. O. Korpusov},
     title = {On the blow-up of internal gravitational waves with non-linear sources},
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     pages = {691--710},
     publisher = {mathdoc},
     volume = {75},
     number = {4},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2011_75_4_a2/}
}
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M. O. Korpusov. On the blow-up of internal gravitational waves with non-linear sources. Izvestiya. Mathematics , Tome 75 (2011) no. 4, pp. 691-710. http://geodesic.mathdoc.fr/item/IM2_2011_75_4_a2/