. A P ] 2 5 Se p 20 06 MINIMAL - MASS BLOWUP SOLUTIONS OF THE MASS - CRITICAL NLS
نویسنده
چکیده
We consider the minimal mass m0 required for solutions to the mass-critical nonlinear Schrödinger (NLS) equation iut + ∆u = μ|u|4/du to blow up. If m0 is finite, we show that there exists a minimal-mass solution blowing up (in the sense of an infinite spacetime norm) in both time directions, whose orbit in Lx(R d) is compact after quotienting out by the symmetries of the equation. A similar result is obtained for spherically symmetric solutions. In a subsequent paper we shall use this compactness result to establish global existence and scattering in Lx(R d) for the defocusing NLS in three and higher dimensions with spherically symmetric data.
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m at h . A P ] 1 6 O ct 2 00 6 MINIMAL - MASS BLOWUP SOLUTIONS OF THE MASS - CRITICAL NLS
We consider the minimal mass m0 required for solutions to the mass-critical nonlinear Schrödinger (NLS) equation iut + ∆u = μ|u|4/du to blow up. If m0 is finite, we show that there exists a minimal-mass solution blowing up (in the sense of an infinite spacetime norm) in both time directions, whose orbit in Lx(R d) is compact after quotienting out by the symmetries of the equation. A similar res...
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تاریخ انتشار 2006