Journal ArticleDOI
Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schrödinger Equation
TLDR
In this paper, the authors consider finite time blow up solutions to the critical nonlinear Schrodinger equation, and prove that the solution splits in two parts: the first part corresponds to the singular part and accumulates a quantized amount of L2 mass at the blow up point, the second part correspond to the regular part and has a strong L2 limit at blow up time.Abstract:
We consider finite time blow up solutions to the critical nonlinear Schrodinger equation Open image in new window For a suitable class of initial data in the energy space H1, we prove that the solution splits in two parts: the first part corresponds to the singular part and accumulates a quantized amount of L2 mass at the blow up point, the second part corresponds to the regular part and has a strong L2 limit at blow up time.read more
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Renormalization and blow-up for wave maps from ²×ℝ to ²
TL;DR: In this paper, a one parameter family of finite time blow-ups to the co-rotational wave maps problem from S-2 x R to S2, parameterized by nu is an element of (1/2, 1).
Journal ArticleDOI
Construction and stability of type i blowup solutions for non-variational semilinear parabolic systems
TL;DR: In this paper, the authors consider the semilinear heat system with no gradient structure taking of the particular form and give a precise description of its blowup profiles, which relies on two-step procedure: the reduction of the problem to a finite dimensional one via a spectral analysis, and then solving the finite dimensional problem by a classical topological argument based on index theory.
Journal Article
On the long time behavior of KDV type equations
TL;DR: In a series of recent papers, Martel and Merle solved the long-standing open problem on the existence of blow up solutions in the energy space for the critical generalized Korteweg-de Vries equation as discussed by the authors.
Posted Content
The instability of Bourgain-Wang solutions for the L^2 critical NLS
TL;DR: In this paper, it was shown that any solution with small super critical mass lies on the boundary of both $H^1$ open sets of global solutions that scatter forward and backwards in time, and solutions that blow up in finite time on the right in the log-log regime exhibited in \cite{MR1, MR4, and R1}.
Journal ArticleDOI
Blow-up dynamics for the self-dual Chern–Simons–Schrödinger equation
TL;DR: In this article , the authors review some recent progress on the blow-up dynamics for the self-dual Chern-Simons-Schrödinger equation within equivariance.
References
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