6533b85ffe1ef96bd12c264b

RESEARCH PRODUCT

Well-posedness of the boundary layer equations

Maria Carmela LombardoMarco SammartinoMarco Cannone

subject

Operator (physics)Applied MathematicsPrandtl numberMathematical analysisAnalysiHalf-spaceSpace (mathematics)Computational Mathematicssymbols.namesakeBoundary layerBoundary layerBoundary layer; Prandtl equations; Mathematics (all); Analysis; Applied MathematicssymbolsMathematics (all)Prandtl equationUniquenessConvection–diffusion equationAnalysisMathematicsVariable (mathematics)

description

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. Theproof 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.

yearjournalcountryeditionlanguage
2004-01-01
10.1137/s0036141002412057http://hdl.handle.net/10447/201329