Well-posedness of the boundary layer equations

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78 Citazioni (Scopus)


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.
Lingua originaleEnglish
pagine (da-a)987-1004
Numero di pagine18
RivistaSIAM Journal on Mathematical Analysis
Stato di pubblicazionePublished - 2004

All Science Journal Classification (ASJC) codes

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