The Zakharov System on the Upper Half-Plane

2025/02/28 by Erdoğan, M. B., Tzirakis, N.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.00129

Abstract

In this paper we study the Zakharov system on the upper half--plane U=\(x ,y)∈ \R²: 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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