publication . Other literature type . Article . 1998

Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space.¶ II. Construction of the Navier-Stokes Solution

Marco Sammartino; Russel E. Caflisch;
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  • Published: 01 Mar 1998
  • Publisher: Springer Science and Business Media LLC
Abstract
This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of the Euler and Prandtl equations, which were constructed in the first paper, plus an error term. This shows that the Navier-Stokes solution goes to an Euler solution outside a boundary layer and to a solution of the Prandtl equations within the boundary layer. The error ter...
Subjects
arXiv: Physics::Fluid DynamicsMathematics::Analysis of PDEs
free text keywords: Mathematical Physics, Statistical and Nonlinear Physics, Stokes flow, Characteristic equation, Laplace's equation, Boundary layer, Stokes' law, symbols.namesake, symbols, Mathematical analysis, Prandtl number, Mathematics, Euler's formula, Nonlinear system
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