Search results for "Inviscid limit"

The inviscid limit and Prandtl's asymptotic expansion for incompressible flows in the half space

2022

The validity of the inviscid limit for the incompressible Navier-Stokes equations is one of the most important and challenging problems in the mathematical theory of fluid dynamics: the motion of inviscid fluids is described by the Euler equations, so, when the viscosity goes to zero, one would expect the convergence of NS solutions to the Euler solutions. However, NS equations are a singular perturbation of the Euler equations: the change of order of the equation implies that fewer boundary conditions can be imposed on the inviscid flows. Therefore, the no-slip boundary conditions, imposed on the NS solutions, are not satisfied by the Euler flow, for which a tangential slip is allowed. Thi…