2024/11/18 by Sakajo, Takashi, Zou, Changjun
#76B47 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2411.15176
We construct a series of classic vorticity solutions for incompressible Euler equation on \mathbb S2, which constitute the C1 type regularization for a general traveling point vortex system. The construction is accomplished by applying tangent mapping on \mathbb S2 and Lyapunov--Schmidt reduction argument. Using the fixed-point theorem and a finite dimensional equation on vortex dynamics, we prove that the vortices are located near a nondegenerate critical point of Kirchhoff--Routh function. Moreover, in the tangent space at each vortex center, the scaled stream function is verified as a perturbation of the ground state for generalized plasma problem. Some other qualitative and quantitative estimates for the regularization series are also obtained in this paper.