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
Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity I: Basic theory
Justin Holmer,Chang Liu +1 more
TL;DR: For focusing point nonlinear Schrodinger equation (NLSE), this article showed that (0.1) shares many properties in common with those previously established for the focusing autonomous translationally-invariant NLS.
Journal ArticleDOI
log–log blow up solutions blow up at exactly m points
TL;DR: In this article, the focusing mass-critical nonlinear Schrodinger equation was studied, and certain solutions which blow up at exactly m points according to the log-log law were constructed.
Journal ArticleDOI
Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions
TL;DR: In this article, a complete classification of the flow near the ground state solitary wave in the energy critical semilinear heat equation was given, based on sole energy estimates deeply.
Journal ArticleDOI
Blow-up profile to the solutions of two-coupled Schrödinger equations
Jianqing Chen,Boling Guo +1 more
TL;DR: Perez-Garcia et al. as mentioned in this paper showed that for the two-coupled Schrodinger equations with harmonic potential, the solution blow up exactly like δ function.
Journal ArticleDOI
Type II blowup in a doubly parabolic Keller–Segel system in two dimensions
TL;DR: In this article, it was shown that each blowup is of type II in the parabolic-parabolic Keller-Segel system in radial case, and that there exists a large class of radial initial data such that the corresponding solutions blow up in finite time.
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.
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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