On the periodic Schrödinger-Debye equation
نویسنده
چکیده
We study local and global well-posedness of the initial value problem for the Schrödinger-Debye equation in the periodic case. More precisely, we prove local well-posedness for the periodic Schrödinger-Debye equation with subcritical nonlinearity in arbitrary dimensions. Moreover, we derive a new a priori estimate for the H norm of solutions of the periodic Schrödinger-Debye equation. A novel phenomena obtained as a by-product of this a priori estimate is the global well-posedness of the periodic Schrödinger-Debye equation in dimensions 1, 2 and 3 without any smallness hypothesis of the H norm of the initial data in the “focusing” case.
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