On the mass-critical generalized KdV equation

Details On the mass-critical generalized KdV equation On the mass-critical generalized KdV equation

2009-07-30

arxiv.org/abs/0907.5412v2

Mathematics

Analysis of PDEs

References added/updated

Scientific paper

We consider the mass-critical generalized Korteweg--de Vries equation $$(\partial_t + \partial_{xxx})u=\pm \partial_x(u^5)$$ for real-valued functions $u(t,x)$. We prove that if the global well-posedness and scattering conjecture for this equation failed, then, conditional on a positive answer to the global well-posedness and scattering conjecture for the mass-critical nonlinear Schr\"odinger equation $(-i\partial_t + \partial_{xx})u=\pm (|u|^4u)$, there exists a minimal-mass blowup solution to the mass-critical generalized KdV equation which is almost periodic modulo the symmetries of the equation. Moreover, we can guarantee that this minimal-mass blowup solution is either a self-similar solution, a soliton-like solution, or a double high-to-low frequency cascade solution.

Affiliated with

Also associated with

No associations

Rating

On the mass-critical generalized 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 On the mass-critical generalized KdV equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the mass-critical generalized KdV equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-266751