scholarly journals Decay of Strong Solutions for 4D Navier-Stokes Equations Posed on Lipschitz Domains

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
N. A. Larkin
Keyword(s):  
Exponential Decay ◽  
Stokes Equations ◽  
Global Solutions ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Navier Stokes ◽  
Lipschitz Domains ◽  
Initial Boundary Value Problems ◽  
Navier Stokes Equations ◽  
Initial Boundary Value

Initial-boundary value problems for 4D Navier-Stokes equations posed on bounded and unbounded 4D parallelepipeds were considered. The existence and uniqueness of regular global solutions on bounded parallelepipeds and their exponential decay as well as the existence, uniqueness, and exponential decay of strong solutions on an unbounded parallelepiped have been established provided that initial data and domains satisfy some special conditions.

Initial–boundary-value problems for one-dimensional compressible Navier–Stokes equations with degenerate transport coefficients

2017 ◽  
Vol 147 (5) ◽  
pp. 935-969 ◽  
Author(s):  
Qing Chen ◽  
Huijiang Zhao ◽  
Qingyang Zou
Keyword(s):  
Boundary Value Problems ◽  
Stokes Equations ◽  
Boundary Value ◽  
Transport Coefficients ◽  
Initial Boundary ◽  
Navier Stokes ◽  
Initial Boundary Value Problems ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Initial Boundary Value

This paper is concerned with the construction of global, non-vacuum, strong, large amplitude solutions to initial–boundary-value problems for the one-dimensional compressible Navier–Stokes equations with degenerate transport coefficients. Our analysis derives the positive lower and upper bounds on the specific volume and the absolute temperature.

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