The Zakharov System on the Upper Half-Plane

M. B. Erdoğan; N. Tzirakis

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arXiv · 2503.00129

The Zakharov System on the Upper Half-Plane

M. B. Erdoğan·N. Tzirakis

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Abstract

In this paper we study the Zakharov system on the upper half--plane $U=\{(x ,y)\in \R^2: y>0\}$ with non-homogenous boundary conditions. In particular we obtain low regularity local well--posedness using the restricted norm method of Bourgain and the Fourier--Laplace method of solving initial and boundary value problems. Moreover we prove that the nonlinear part of the solution is in a smoother space than the initial data. To our knowledge this is the first paper which establishes low regularity results for the 2d initial-boundary value Zakharov system.

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M. B. Erdoğan, N. Tzirakis. 2025-02-28. The Zakharov System on the Upper Half-Plane. https://arxiv.org/abs/2503.00129

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