scholarly journals Global regularity and asymptotic behavior of modified Navier-Stokes equations with fractional dissipation

2012 ◽  
Vol 32 (1) ◽  
pp. 57-79 ◽  
Author(s):  
Bo-Qing Dong ◽  
◽  
Juan Song
Keyword(s):  
Asymptotic Behavior ◽  
Global Regularity ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER–STOKES EQUATIONS FOR A 1D ISOTHERMAL VISCOUS GAS

2008 ◽  
Vol 18 (08) ◽  
pp. 1383-1408 ◽  
Author(s):  
YUMING QIN ◽  
YANLI ZHAO
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Stokes Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Asymptotic Behavior Of Solutions ◽  
Navier Stokes Equations ◽  
Viscous Gas ◽  
Initial Boundary Value

In this paper, we prove the global existence and asymptotic behavior of solutions in Hi(i = 1, 2) to an initial boundary value problem of a 1D isentropic, isothermal and the compressible viscous gas with an non-autonomous external force in a bounded region.

Large-frequency global regularity for the incompressible Navier–Stokes equation

1999 ◽  
Vol 129 (5) ◽  
pp. 903-912
Author(s):  
Joel D. Avrin
Keyword(s):  
Boundary Conditions ◽  
Global Regularity ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Thin Domains ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Incompressible Navier Stokes Equation

We obtain global existence and regularity of strong solutions to the incompressible Navier–Stokes equations for a variety of boundary conditions in such a way that the initial and forcing data can be large in the high-frequency eigenspaces of the Stokes operator. We do not require that the domain be thin as in previous analyses. But in the case of thin domains (and zero Dirichlet boundary conditions) our results represent a further improvement and refinement of previous results obtained.

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