Well-posedness of the two-dimensional generalized Benjamin-Bona-Mahony equation on the upper half plane

TL;DR

This paper proves the global well-posedness of the two-dimensional Benjamin-Bona-Mahony equations with general flux functions in the upper half-plane, ensuring solutions exist, are unique, and depend continuously on initial and boundary data.

Contribution

It establishes the global well-posedness for a class of two-dimensional Benjamin-Bona-Mahony equations with general flux functions in the upper half-plane.

Findings

Global well-posedness in Sobolev spaces

Solutions become classical with more regular data

Continuous dependence on initial and boundary data

Abstract

This paper focuses on the two-dimensional Benjamin-Bona-Mahony and Benjamin-Bona-Mahony-Burgers equations with a general flux function. The aim is at the global (in time) well-posedness of the initial-and boundary-value problem for these equations defined in the upper half-plane. Under suitable growth conditions on the flux function, we are able to establish the global well-posedness in a Sobolev class. When the initial- and boundary-data become more regular, the corresponding solutions are shown to be classical. In addition, the continuous dependence on the data is also obtained.