A Characteristic-Galerkin Method for the Navier-Stokes Equations in Thin Domains with Free Boundaries

1995 ◽  
pp. 201-213 ◽  
Author(s):  
Giovanni M. Cornetti
Keyword(s):  
Galerkin Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Free Boundaries ◽  
Thin Domains ◽  
Navier Stokes Equations

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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