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# The Mass-critical Nonlinear Schr¨odinger Equation with Radial Data in Dimensions Three and Higher

@inproceedings{Visan2008TheMN, title={The Mass-critical Nonlinear Schr¨odinger Equation with Radial Data in Dimensions Three and Higher}, author={Monica Visan and Xiaoyi Zhang}, year={2008} }

- Published 2008

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iut +∆u = ±|u|4/du for large spherically symmetric Lx(R d) initial data in dimensions d ≥ 3. In the focusing case we require that the mass is strictly less than that of the ground state. As a consequence, we obtain that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time.

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