SELF-SIMILAR SOLUTIONS AND CRITICAL SPACES FOR THE MODIFIED KORTEWEG-DE VRIES EQUATION

We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted W 1,8 around

For smooth and decaying data, this problem (the so-called soliton resolution conjecture) can be studied via the inverse transform method ((mKdV) is integrable): for generic such

Self-similar solutions play an important role for the (mKdV) flow: they exhibit an explicit blow up behavior, and are also related with the long time description of solutions.. Even

Obviously, we shrank considerably the critical space by taking smooth perturbations of self- similar solutions, but the above result still shows some kind of stability of

The goal of this note is to construct a class of traveling solitary wave solutions for the compound Burgers-Korteweg-de Vries equation by means of a hyperbolic ansatz.. Equation (1)

These generalise the famous result for the mean curvature flow by Huisken [20], although in that case and for some other flows no curvature pinching condition on the

[Gi] GIGA, Y., Solutions for semilinear parabolic equations in L p and regularity of weak solutions of the Navier-Stokes equations with data in L p.. &

Another way to view this equation and the degeneracy comes from the nonlinear damping problem for Euler equations with vacuum.. We believe that the study in this paper will be useful