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.
Keywords:hydrodynamic system with nonlinear viscosity, blow-up of solutions, Navier–Stokes system, nonlinear source, energy method, Galerkin approximation method, Banach space, Gronwall–Bellman lemma.
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