We consider the mild solutions of the Prandtl equations on the half space. Requiring analyticity only with respect to the tangential variable, we prove the short time existence and the uniqueness of the solution in the proper function space. The proof is achieved applying the abstract Cauchy-Kowalewski theorem to the boundary layer equations once the convection-diffusion operator is explicitly inverted. This improves the result of [M. Sammartino and R. E. Caflisch, Comm. Math. Phys., 192 (1998), pp. 433-461], as we do not require analyticity of the data with respect to the normal variable.
Lombardo, M., Cannone, M., Sammartino, M. (2004). Well-posedness of the boundary layer equations. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 35(4), 987-1004 [10.1137/S0036141002412057].
Well-posedness of the boundary layer equations
LOMBARDO, Maria Carmela;SAMMARTINO, Marco Maria Luigi
2004-01-01
Abstract
We consider the mild solutions of the Prandtl equations on the half space. Requiring analyticity only with respect to the tangential variable, we prove the short time existence and the uniqueness of the solution in the proper function space. The proof is achieved applying the abstract Cauchy-Kowalewski theorem to the boundary layer equations once the convection-diffusion operator is explicitly inverted. This improves the result of [M. Sammartino and R. E. Caflisch, Comm. Math. Phys., 192 (1998), pp. 433-461], as we do not require analyticity of the data with respect to the normal variable.File | Dimensione | Formato | |
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