Construction of L² log-log blowup solutions for the mass critical nonlinear Schrödinger equation

2020/10/15 by Fan, Chenjie, Mendelson, Dana · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.07821

Abstract

In this article, we study the log-log blowup dynamics for the mass critical nonlinear Schrödinger equation on ℝ² under rough but structured random perturbations at L²(ℝ²) regularity. In particular, by employing probabilistic methods, we provide a construction of a family of L²(ℝ²) regularity solutions which do not lie in any H^s(ℝ²) for any s>0, and which blowup according to the log-log dynamics.

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