Well-posedness of The Prandtl Equation in Sobolev Spaces

Details Well-posedness of The Prandtl Equation in Sobolev Spaces Well-posedness of The Prandtl Equation in Sobolev Spaces

2012-03-27

arxiv.org/abs/1203.5991v1

Mathematics

Analysis of PDEs

Scientific paper

We develop a new approach to study the well-posedness theory of the Prandtl equation in Sobolev spaces by using a direct energy method under a monotonicity condition on the tangential velocity field instead of using the Crocco transformation. Precisely, we firstly investigate the linearized Prandtl equation in some weighted Sobolev spaces when the tangential velocity of the background state is monotonic in the normal variable. Then to cope with the loss of regularity of the perturbation with respect to the background state due to the degeneracy of the equation, we apply the Nash-Moser-Hormander iteration to obtain a well-posedness theory of classical solutions to the nonlinear Prandtl equation when the initial data is a small perturbation of a monotonic shear flow.

Affiliated with

Also associated with

No associations

Rating

Well-posedness of The Prandtl Equation in Sobolev Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Well-posedness of The Prandtl Equation in Sobolev Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Well-posedness of The Prandtl Equation in Sobolev Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-641132