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
Citations
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Journal ArticleDOI
On one blow up point solutions to the critical nonlinear schrödinger equation
Frank Merle,Pierre Raphaël +1 more
TL;DR: In this paper, the L2 critical nonlinear Schrodinger equation was considered and the authors proved the existence and stability of large L2 mass log-log type solutions which are believed to describe the generic blow up dynamics.
Journal ArticleDOI
Non radial type II blow up for the energy supercritical semilinear heat equation
TL;DR: In this paper, a non-radial construction of a solution blowing up by concentration of a stationary state in the supercritical regime was presented, which generalizes previous works on the existence of type II blow-up solutions.
Journal ArticleDOI
The sharp threshold and limiting profile of blow-up solutions for a Davey–Stewartson system
TL;DR: The blow-up threshold of the Cauchy problem for the Davey-Stewartson system was investigated in this article, where the authors derived the best constant of a Gagliardo-Nirenberg type inequality and the variational character of the ground state.
Journal ArticleDOI
Global existence and uniqueness results for weak solutions of the focusing mass-critical nonlinear Schrödinger equation
TL;DR: In this paper, a semi-Strichartz class solution was introduced for the focusing mass-critical NLS problem in high dimensions d ≥ 4, and the equivalence of the Strichartz class and the strong solution class was established.
Journal ArticleDOI
Orbital stability and singularity formation for Vlasov–Poisson systems
TL;DR: In this paper, Lemou et al. considered the nonlinear stability of steady states solutions within the framework of concentration compactness techniques and obtained the orbital stability in the energy space of the polytropes which are ground state type stationary solutions.
References
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Uniqueness of positive solutions of Δu−u+up=0 in Rn
TL;DR: In this article, the uniqueness of the positive, radially symmetric solution to the differential equation Δu−u+up=0 (with p>1) in a bounded or unbounded annular region in Rn for all n ≥ 1, with the Neumann boundary condition on the inner ball and the Dirichlet boundary condition decaying to zero in the case of an unbounded region, was established.
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Nonlinear Schrödinger equations and sharp interpolation estimates
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