APRIORI CRITERION FOR INVISCID LIMIT OF NAVIER-STOKES EQUATIONS

We consider the inviscid limit of the Navier-Stokes equations in a bounded domain. After mentioning the review and general difficulty of this problem, we give some integrability conditions on velocity fields which assures the convergence of the Navier-Stokes equations to the Euler equations with the no-slip conditions.

[1]  On the inviscid limit for 2D incompressible flow with Navier friction condition , 2003, math/0307295.

[2]  William Thomson,et al.  Mathematical and physical papers , 1880 .

[3]  Andro Mikelić,et al.  On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions , 1998 .

[4]  P. Lions.  Mathematical topics in fluid mechanics , 1996 .

[5]  Willi Jäger,et al.  Couette Flows over a Rough Boundary and Drag Reduction , 2001 .

[6]  R. Temam.  Navier-Stokes Equations , 1977 .

[7]  Willi Jäger,et al.  On the Roughness-Induced Effective Boundary Conditions for an Incompressible Viscous Flow , 2001 .

[8]  Mario Pulvirenti,et al.  Mathematical Theory of Incompressible Nonviscous Fluids , 1993 .

[9]  D. Iftimie,et al.  Inviscid limits for the Navier–Stokes equations with Navier friction boundary conditions , 2006 .

[10]  Tosio Kato.  Nonstationary flows of viscous and ideal fluids in R3 , 1972 .

[11]  Chemin Jean-Yves.  A remark on the inviscid limit for two-dimensional incompressible fluids , 1996 .

[12]  Hyunseok Kim,et al.  Unique solvability for the stationary Navier-Stokes equations in exterior domains , 2009 .

[13]  R. Elrick,et al.  Tracer Study of Pipe Flow Behavior to within Two Microns of the Wall , 1966 .

[14]  James P. Kelliher.  Navier-Stokes Equations with Navier Boundary Conditions for a Bounded Domain in the Plane , 2006, SIAM J. Math. Anal..

[15]  Russel E. Caflisch,et al.  Zero Viscosity Limit for Analytic Solutions, of the Navier-Stokes Equation on a Half-Space.¶I. Existence for Euler and Prandtl Equations , 1998 .

[16]  Tosio Kato,et al.  Remarks on Zero Viscosity Limit for Nonstationary Navier- Stokes Flows with Boundary , 1984 .