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
More filters
Journal ArticleDOI
Low regularity blowup solutions for the mass-critical NLS in higher dimensions
Chenmin Sun,Jiqiang Zheng +1 more
TL;DR: In this paper, Zhang et al. studied the H s -stability of the log-log blowup regime for the focusing mass-critical nonlinear Schrodinger equations in R d with d ≥ 3.
Journal ArticleDOI
On effective solutions of the nonlinear Schrödinger equation
TL;DR: In this article, a nonlinear Schr?dinger type equation with specific initial-boundary conditions in the infinite domain is considered and the equation is reduced to an equivalent system of partial differential equations and studied in the case of solitary waves.
Journal ArticleDOI
Low regularity blowup solutions for the mass-critical NLS in higher dimensions
Chenmin Sun,Jiqiang Zheng +1 more
TL;DR: In this article, Zhang et al. studied the stability of the log-log blowup for focusing mass-critical nonlinear Schrodinger equations in higher dimensions below the energy class.
Posted Content
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.
Posted Content
The $L^{2}$ weak sequential convergence of radial mass critical NLS solutions with mass above the ground state
TL;DR: In this paper, the authors studied the non-scattering solution of the nonlinear Schrodinger equation with mass just above the ground state, and showed that there exists a time sequence such that the solution weakly converges to ground state up to scaling and phase transformation.
References
More filters
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.
Related Papers (5)
On universality of blow-up profile for L 2 critical nonlinear Schrödinger equation
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
Frank Merle,Pierre Raphaël +1 more