Almost Global Existence for the Prandtl Boundary Layer Equations
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چکیده
We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H1 space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within ε of a stable profile, then the unique solution of the Cauchy problem can be extended at least up to time Tε exp(ε−1/ log(ε−1)).
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تاریخ انتشار 2015