Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8256413 | Physica D: Nonlinear Phenomena | 2015 | 11 Pages |
Abstract
In this article we consider the Euler-α system as a regularization of the incompressible Euler equations in a smooth, two-dimensional, bounded domain. For the limiting Euler system we consider the usual non-penetration boundary condition, while, for the Euler-α regularization, we use velocity vanishing at the boundary. We also assume that the initial velocities for the Euler-α system approximate, in a suitable sense, as the regularization parameter αâ0, the initial velocity for the limiting Euler system. For small values of α, this situation leads to a boundary layer, which is the main concern of this work. Our main result is that, under appropriate regularity assumptions, and despite the presence of this boundary layer, the solutions of the Euler-α system converge, as αâ0, to the corresponding solution of the Euler equations, in L2 in space, uniformly in time. We also present an example involving parallel flows, in order to illustrate the indifference to the boundary layer of the αâ0 limit, which underlies our work.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Milton C. Lopes Filho, Helena J. Nussenzveig Lopes, Edriss S. Titi, Aibin Zang,