2019/10/09 by Daomin Cao, Guodong Wang, Cao, Daomin +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1910.03758
openalex publication_date 2019/10/09 · openalex created_date 2019/10/18 · openalex updated_date 2026/07/28
In this paper, we consider steady Euler flows in a planar bounded domain in which the vorticity is sharply concentrated in a finite number of disjoint regions of small diameter. Such flows are closely related to the point vortex model and can be regarded as desingularization of point vortices. By an adaption of the vorticity method, we construct a family of steady Euler flows in which the vorticity is concentrated near a global minimum point of the Robin function of the domain, and the corresponding stream function satisfies a semilinear elliptic equation with a given profile function. Furthermore, for any given isolated minimum point (x1,⋅⋅⋅,xk) of the Kirchhoff-Routh function of the domain, we prove that there exists a family of steady Euler flows whose vorticity is supported in k small regions near xi, and near each xi the corresponding stream function satisfies a semilinear elliptic equation with a given profile function.