Strongly interacting blow up bubbles for the mass critical NLS

Abstract

We construct a new class of multi-solitary wave solutions for the mass critical two dimensional nonlinear Schrodinger equation (NLS). Given any integer K>1, there exists a global (for positive time) solution of (NLS) that decomposes asymptotically into a sum of solitary waves centered at the vertices of a K-sided regular polygon and concentrating at a logarithmic rate in large time. This solution blows up in infinite time with logarithmic rate. Using the pseudo-conformal transform, this yields the first example of solution blowing up in finite time with a rate strictly above the pseudo-conformal one. Such solution concentrates K bubbles at a point. These special behaviors are due to strong interactions between the waves, in contrast with previous works on multi-solitary waves of (NLS) where interactions do not affect the blow up rate.

References in corpus (4)

• Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5
• Type II blow up manifolds for the energy supercritical wave equation
• Log-log blow up solutions blow up at exactly m points
• Minimal mass blow up solutions for a double power nonlinear Schrödinger equation

Cited by in corpus (6)

• Construction of multi-solitons for the energy-critical wave equation in dimension 5
• Dynamics of strongly interacting unstable two-solitons for generalized Korteweg-de Vries equations
• Blow-up solutions for $L^2$-supercritical gKdV equations with exactly $k$ blow-up points
• Strongly interacting multi-solitons with logarithmic relative distance for gKdV equation
• Log-log blow up solutions blow up at exactly m points
• Global Dynamics of solutions with group invariance for the nonlinear Schrödinger equation