Special Session 15: Qualitative properties for solutions to nonlinear elliptic and parabolic equations
Existence and local uniqueness of solutions to fractional equations with application to fluid dynamics
Guolin Qin
Academy of Mathematics and Systems Science, Chinese Academy of Sciences Peoples Rep of China
Co-Author(s): Daomin Cao, Shanfa Lai, Weicheng Zhan, Changjun Zou
Abstract:
This talk is concerned with the study of fractional elliptic equations arising from fluid dynamics. Taking the generalized surface quasi-geostrophic (gSQG) equation as a prototype, we investigate the existence, asymptotic behavior, local uniqueness, and nonlinear orbital stability of traveling-wave solutions with small propagation speeds.