On the existence of vortex-wave systems to inviscid gSQG equation
Daomin Cao, Shanfa Lai, Changjun Zou
TL;DR
This paper investigates the existence of vortex-wave systems in inviscid generalized surface quasi-geostrophic (gSQG) flows, addressing mathematical challenges through a novel reduction method and analyzing asymptotic behaviors.
Contribution
It introduces a modified reduction method to prove the existence of vortex-wave systems with point vortices and compact support vortices in inviscid gSQG flows, overcoming singularities and energy issues.
Findings
Established existence of vortex-wave systems in inviscid gSQG flows.
Analyzed asymptotic properties of the vortex-wave systems.
Developed a new reduction method to handle singularities.
Abstract
We study the existence of different vortex-wave systems for inviscid gSQG flow, where the total circulation are produced by point vortices and vortices with compact support. To overcome several difficulties caused by the singular formulation and infinite kinetic energy, we introduce a modified reduction method. Several asymptotic properties of the system are also given.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Navier-Stokes equation solutions · Stability and Controllability of Differential Equations