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 the $L^2$-critical nonlinear Schrödinger 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
Regularizing nonlinear Schroedinger equations through partial off-axis variations
TL;DR: In this paper, the authors study a class of focusing nonlinear Schroedinger-type equations derived by Dumas, Lannes and Szeftel within the mathematical description of high intensity laser beams.
Posted Content
Some remarks on the nonlinear Schr\"odinger equation with fractional dissipation
Mohamad Darwich,Luc Molinet +1 more
TL;DR: In this paper, the authors considered the Cauchy problem for the nonlinear Schrodinger equation with a fractional dissipation and proved the global existence or the existence of finite time blowup dynamics with the log-log blow-up speed.
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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