Abstract
Sufficient conditions for the blow-up of solutions of the hydrodynamic systems proposed by Ladyzhenskaya in 1966 with nonlinear viscosity and exterior sources are obtained. Questions relating to local solvability and uniqueness are answered using the finite-dimensional Galerkin approximation method The energy method, which was first applied to hydrodynamic systems by Korpusov and Sveshnikov, is used to obtain estimates of the blow-up time and blow-up rate. The determining role of nonlinear exterior sources, not viscous or hydrodynamic nonlinearity, on the occurrence of the blow-up effect is shown.
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Original Russian Text © E. V. Yushkov, 2014, published in Matematicheskie Zametki, 2014, Vol. 95, No. 4, pp. 615–629.
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Yushkov, E.V. Blow-up in systems with nonlinear viscosity. Math Notes 95, 552–564 (2014). https://doi.org/10.1134/S0001434614030274
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DOI: https://doi.org/10.1134/S0001434614030274