Special Session 73: Nonlinear elliptic and parabolic equations and related functional inequalities
Recent progress in the study of concentrated helical vortices of 3d incompressible Euler equations
Jie Wan
Beijing Institute of Technology
Peoples Rep of China
Co-Author(s):    Daomin Cao, Rui Li, Guolin Qin
Abstract:
In this talk, we first introduce recent progress of the existence of concentrated helical vortices of 3d incompressible Euler equations when the orthogonality condition holds. Then, in case that the orthogonality condition fails, we prove the existence of concentrated helical vortices of 3d incompressible Euler equations in infinite cylinders. As parameter $\varepsilon\to0$, the vorticity concentrates near a helix evolved by the vortex filament equations.
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