A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations

Details A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations

2007-01-24

arxiv.org/abs/math/0701681v1

Mathematics

Analysis of PDEs

Scientific paper

We study the well-posedness of the initial value problem for a wide class of singular evolution equations. We prove a general well-posedness theorem under three assumptions easy to check: the first controls the singular part of the equation, the second the behavior of the nonlinearities, and the third one assumes that an energy estimate can be found for the linearized system. We allow losses of derivatives in this energy estimate and therefore construct a solution by a Nash-Moser iterative scheme. As an application to this general theorem, we prove the well-posedness of the Serre and Green-Naghdi equation and discuss the problem of their validity as asymptotic models for the water-waves equations.

Affiliated with

Also associated with

No associations

Rating

A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations 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 A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-603757