Local well-posedness for the Zakharov system on multidimensional torus

Abstract

The initial value problem of the Zakharov system on two dimensional torus with general period is shown to be locally well-posed in the Sobolev spaces of optimal regularity, including the energy space. Proof relies on a standard iteration argument using the Bourgain norms. The same strategy is also applicable to three and higher dimensional cases.

35 pages, 3 figures

References in corpus (2)

• Convolutions of singular measures and applications to the Zakharov system
• Local ill-posedness of the 1D Zakharov system

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• Smoothing and Global Attractors for the Zakharov System on the Torus
• Sharp spherically averaged Strichartz estimates for the Schrödinger equation