# Blow-up solutions on a sphere for the 3D quintic NLS in the energy space

@inproceedings{Holmer2010BlowupSO, title={Blow-up solutions on a sphere for the 3D quintic NLS in the energy space}, author={Justin Holmer and Svetlana Roudenko}, year={2010} }

We prove that if u(t) is a log-log blow-up solution, of the type studied by Merle-Raphael [14], to the L critical focusing NLS equation i∂tu+∆u+|u|u = 0 with initial data u0 ∈ H(R) in the cases d = 1, 2, then u(t) remains bounded in H away from the blow-up point. This is obtained without assuming that the initial data u0 has any regularity beyond H(R). As an application of the d = 1 result, we construct an open subset of initial data in the radial energy space H rad(R) with corresponding… CONTINUE READING

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## Global Behavior Of Finite Energy Solutions To The Focusing Nonlinear Schrodinger Equation In d Dimension

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CITES BACKGROUND & METHODS

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## Log-log blow up solutions blow up at exactly m points

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CITES METHODS

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 18 REFERENCES

## Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schrödinger Equation

VIEW 10 EXCERPTS

HIGHLY INFLUENTIAL

## Refinements of Strichartz' inequality and applications to 2D-NLS with critical nonlinearity

VIEW 11 EXCERPTS

HIGHLY INFLUENTIAL

## Standing Ring Blow up Solutions to the N-Dimensional Quintic Nonlinear Schrödinger Equation

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## Existence and stability of a solution blowing up on a sphere for an $L^2$-supercritical nonlinear Schrödinger equation

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## On the Formation of Singularities in Solutions of the Critical Nonlinear Schrödinger Equation

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## The Inhomogeneous Dirichlet Problem in Lipschitz Domains

VIEW 2 EXCERPTS

HIGHLY INFLUENTIAL

## Harmonic analysis: Real-variable methods

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension.

VIEW 2 EXCERPTS

HIGHLY INFLUENTIAL