Geodesic
Blow-Up in Systems with Nonlinear Viscosity
Matematičeskie zametki, Tome 95 (2014) no. 4, pp. 615-629

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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. 
@article{MZM_2014_95_4_a11,
     author = {E. V. Yushkov},
     title = {Blow-Up in {Systems} with {Nonlinear} {Viscosity}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {615--629},
     publisher = {mathdoc},
     volume = {95},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_4_a11/}
}
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E. V. Yushkov. Blow-Up in Systems with Nonlinear Viscosity. Matematičeskie zametki, Tome 95 (2014) no. 4, pp. 615-629. http://geodesic.mathdoc.fr/item/MZM_2014_95_4_a11/