Existence of steady multiple vortex patches to the vortex-wave system

2018/05/07 by Daomin Cao, Guodong Wang, Cao, Daomin +1
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.1805.02323

openalex publication_date 2018/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove the existence of steady multiple vortex patch solutions to the vortex-wave system in a planar bounded domain. The construction is performed by solving a certain variational problem for the vorticity and studying its asymptotic behavior as the vorticity strength goes to infinity.

Related

• Uniqueness of planar vortex patch in incompressible steady flow
• Steady double vortex patches with opposite signs in a planar ideal fluid
• Steady vortex patches on flat torus with a constant background vorticity
• Steady vortex patches near a rotating flow with constant vorticity in a planar bounded domain
• On 3-D vortex patches in bounded domains