2 00 4 Global Existence and Scattering for Rough Solutions of a Nonlinear Schrödinger Equation on R 3
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چکیده
We prove global existence and scattering for the defocusing, cubic nonlinear Schrödinger equation in H s (R 3) for s > 4 5. The main new estimate in the argument is a Morawetz-type inequality for the solution φ. This estimate bounds φ(x, t) L 4 x,t (R 3 ×R) , whereas the well-known Morawetz-type estimate of Lin-Strauss controls ∞ 0 R 3 (φ(x,t)) 4 |x| dxdt.
منابع مشابه
. A P ] 2 3 Ja n 20 03 GLOBAL EXISTENCE AND SCATTERING FOR ROUGH SOLUTIONS OF A NONLINEAR SCHRÖDINGER EQUATION ON R 3
We prove global existence and scattering for the defocusing, cubic nonlinear Schrödinger equation in H s (R 3) for s > 4 5. The main new estimate in the argument is a Morawetz-type inequality for the solution φ. This estimate bounds φ(x, t) L 4 x,t (R 3 ×R) , whereas the well-known Morawetz-type estimate of Lin-Strauss controls ∞ 0 R 3 (φ(x,t)) 4 |x| dxdt.
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تاریخ انتشار 2004