Null structures and degenerate dispersion relations in two space dimensions

Yuqiu Fu; Daniel Tataru

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arXiv · 1801.00099

Null structures and degenerate dispersion relations in two space dimensions

Yuqiu Fu·Daniel Tataru

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Abstract

Motivated by water-wave problems, in this paper we consider a class of nonlinear dispersive PDEs in 2D with cubic nonlinearities, whose dispersion relations are radial and have vanishing Guassian curvature on a circle. For such a model we identify certain null structures for the cubic nonlinearity, which suffice in order to guarantee global scattering solutions for the small data problem. Our null structures in the power-type nonlinearity are weak, and only eliminate the worst nonlinear interaction. Such null structures arise naturally in some water-wave problems.

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Yuqiu Fu, Daniel Tataru. 2017-12-30. Null structures and degenerate dispersion relations in two space dimensions. https://arxiv.org/abs/1801.00099

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