Blow-up in systems with nonlinear viscosity

被引：0

作者：

E. V. Yushkov

机构：

[1] Moscow State University,

来源：

Mathematical Notes | 2014年 / 95卷

关键词：

hydrodynamic system with nonlinear viscosity; blow-up of solutions; Navier-Stokes system; nonlinear source; energy method; Galerkin approximation method; Banach space; Gronwall-Bellman lemma;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：552 / 564

页数：12

共 9 条

[1]

Korpusov M O(2009)Blow-up of Oskolkov’s system of equations Mat. Sb. 200 83-108

[2]

Sveshnikov A G(1984)Remarks on the breakdown of smooth solutions for the 3-D Euler equation Comm. Math. Phys. 94 61-66

[3]

Beale J T(2004)Blowup in a the three-dimensional vector model for the Euler equations Comm. Pure Appl. Math. 57 705-725

[4]

Kato T(2012)On the blow-up of a solution of a non-local system of equations of hydrodynamic type Izv. Ross. Akad. Nauk Ser. Mat. 76 201-224

[5]

Majada A(2012)On the blow-up of solutions of problems of hydrodynamic type with a singular source Zh. Vychisl. Mat. i Mat. Fiz. 52 1523-1535

[6]

Friedlander S(undefined)undefined undefined undefined undefined-undefined

[7]

Pavlović N(undefined)undefined undefined undefined undefined-undefined

[8]

Yushkov E V(undefined)undefined undefined undefined undefined-undefined

[9]

Yushkov E V(undefined)undefined undefined undefined undefined-undefined

← 1 →