An improved local wellposedness result for the modified KdV equation
Axel Gruenrock
Abstract
The Cauchy problem for the modified KdV equation is shown to be locally well posed for data u0 in the space (Hrs) defined by the norm ||u0||:=||<ξ>s (u0)||Lr', provided 4/3 < r 2, s 1/2 - 1/(2r). For r=2 this coincides with the best possible result on the Hs - 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.
Create a lesson
Related papers
Positive normalized solutions for a singular regularized p(x)-Laplacian Dirichlet problem
Mustafa Avci
Regularity for axisymmetric Navier-Stokes with an Euler length
Peter Constantin, Mihaela Ignatova, Vlad Vicol
Existence of strong initial traces for stochastic conservation laws
Marko Erceg, Nikola Konatar, Kenneth Karlsen et al.
Asymptotics of nonlocal nonlinear Robin energies
Serena Dipierro, Giuseppe Spadaro, Enrico Valdinoci
Discontinuity of the Vlasov--Poisson Flow in LxpLv∞
Ke Chen, In-Jee Jeong, Quoc-Hung Nguyen et al.
Dense orbits for scale-invariant rotationally symmetric solutions of the 2D Euler equations
Ibrahim Suleiman