Year: 2019
Type: article
Abstract: The vortex-wave system describes the motion of a two-dimensional ideal fluid in which the vorticity includes continuously distributed vorticity, which is called the background vorticity, and a finite number of concentrated vortices. In this paper we restrict ourselves to the case of a single point vortex in a planar bounded domain. We prove that there exists a family of steady solutions to this system whose background vorticity is a vortex patch with prescribed distribution. Moreover, we show that these vortex patches ‘shrink’ to a minimum point of the Kirchhoff–Routh function as the strength parameter of the background vorticity goes to infinity.
Source: Nonlinearity
Authors: Daomin Cao, Guodong Wang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2801681769