An improved local wellposedness result for the modified KdV equation

Details An improved local wellposedness result for the modified KdV equation An improved local wellposedness result for the modified KdV equation

2003-12-11

arxiv.org/abs/math/0312238v1

Mathematics

Analysis of PDEs

14 pages

Scientific paper

The Cauchy problem for the modified KdV equation is shown to be locally well posed for data u_0 in the space \hat(H^r_s) defined by the norm ||u_0||:=||<\xi>^s \hat(u_0)||_L^r', provided 4/3 < r \le 2, s \ge 1/2 - 1/(2r). For r=2 this coincides with the best possible result on the H^s - scale due to Kenig, Ponce and Vega. The proof uses an appropriate variant of the Fourier restriction norm method and linear as well as bilinear estimates for the solutions of the Airy equation.

Affiliated with

Also associated with

No associations

Rating

An improved local wellposedness result for the modified KdV equation 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 An improved local wellposedness result for the modified KdV equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An improved local wellposedness result for the modified KdV equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-726273