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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Dissertation
On the dynamics of energy-critical focusing wave equations
TL;DR: In this article, the authors studied the global behavior of solutions of the energy-critical focusing nonlinear wave equation, with a special emphasis on the description of the dynamics in the energy space.
Journal ArticleDOI
Critical non-linear dispersive equations: global existence, scattering, blow-up and universal profiles
TL;DR: In this article, the authors discuss recent progress in the understanding of the global behavior of solutions to critical non-linear dispersive equations, focusing on global existence, scattering and finite time blow-up.
Posted Content
On the $L^{2}$-critical nonlinear Schr\"odinger Equation with a nonlinear damping
TL;DR: In this article, the Cauchy problem for the nonlinear Schrodinger equation with a nonlinear damping was considered and the global existence or the existence of finite time blowup dynamics with the log-log blow-up speed was proved.
Posted Content
Multi-bubble Bourgain-Wang solutions to nonlinear Schr\"odinger equation
TL;DR: In this article, the authors considered a general class of focusing nonlinear Schr\"odinger equations with lower order perturbations, for which the pseudo-conformal symmetry and the conservation law of energy are absent.
References
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Journal ArticleDOI
Nonlinear scalar field equations, I existence of a ground state
TL;DR: In this article, a constrained minimization method was proposed for the case of dimension N = 1 (Necessary and sufficient conditions) for the zero mass case, where N is the number of dimensions in the dimension N.
BookDOI
The nonlinear Schrödinger equation : self-focusing and wave collapse
TL;DR: In this article, the authors present a basic framework to understand structural properties and long-time behavior of standing wave solutions and their relationship to a mean field generation and acoustic wave coupling.
Journal ArticleDOI
On a class of nonlinear Schro¨dinger equations
TL;DR: In this paper, the existence of standing wave solutions of nonlinear Schrodinger equations was studied and sufficient conditions for nontrivial solutionsu ∈W¯¯¯¯1,2(ℝ�姫 n ) were established.
Journal ArticleDOI
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.
Journal ArticleDOI
Nonlinear Schrödinger equations and sharp interpolation estimates
TL;DR: In this paper, a sharp sufficient condition for global existence for the nonlinear Schrodinger equation is obtained for the case σ = 2/N. This condition is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of Nirenberg and Gagliardo.
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