Inter-critical NLS: critical $\dot{H}^s$-bounds imply scattering

Jason Murphy

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arXiv · 1209.4582

Inter-critical NLS: critical $\dot{H}^s$-bounds imply scattering

Jason Murphy

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Abstract

We consider a class of power-type nonlinear Schr\"odinger equations for which the power of the nonlinearity lies between the mass- and energy-critical exponents. Following the concentration-compactness approach, we prove that if a solution $u$ is bounded in the critical Sobolev space throughout its lifespan, that is, $u\in L_t^\infty \dot{H}_x^{s_c}$, then $u$ is global and scatters.

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Jason Murphy. 2012-09-20. Inter-critical NLS: critical $\dot{H}^s$-bounds imply scattering. https://arxiv.org/abs/1209.4582

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