scholarly journals The topological degree method for equations of the Navier-Stokes type

1997 ◽  
Vol 2 (1-2) ◽  
pp. 1-45 ◽  
Author(s):  
V. T. Dmitrienko ◽  
V. G. Zvyagin
Keyword(s):  
Boundary Value Problem ◽  
Stokes Equations ◽  
Degree Theory ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Existence Of Weak Solutions ◽  
Initial Boundary Value ◽  
Topological Degree Method

We obtain results of existence of weak solutions in the Hopf sense of the initial-boundary value problem for the generalized Navier-Stokes equations containing perturbations of retarded type. The degree theory for mapsA−g, whereAis invertible andgis𝒜-condensing, is used.

scholarly journals Global Solutions to the Spherically Symmetric Compressible Navier-Stokes Equations with Density-Dependent Viscosity

2012 ◽  
Vol 2012 ◽  
pp. 1-22
Author(s):  
Ruxu Lian ◽  
Lan Huang ◽  
Jian Liu
Keyword(s):  
Boundary Value Problem ◽  
Stokes Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Exterior Problem ◽  
Navier Stokes Equations ◽  
Initial Boundary Value ◽  
Dependent Viscosity

We consider the exterior problem and the initial boundary value problem for the spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient in this paper. For regular initial density, we show that there exists a unique global strong solution to the exterior problem or the initial boundary value problem, respectively. In particular, the strong solution tends to the equilibrium state ast→+∞.

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