. A P ] 1 4 Ju n 20 10 SCATTERING THRESHOLD FOR THE FOCUSING NONLINEAR KLEIN - GORDON EQUATION
نویسنده
چکیده
We show scattering versus blow-up dichotomy below the ground state energy for the focusing nonlinear Klein-Gordon equation, in the spirit of KenigMerle for the H critical wave and Schrödinger equations. Our result includes the H critical case, where the threshold is given by the ground state for the massless equation, and the 2D square-exponential case, where the mass for the ground state may be modified, depending on the constant in the sharp Trudinger-Moser inequality. The main difficulty is the lack of scaling invariance in both the linear and the nonlinear terms.
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تاریخ انتشار 2010