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- W4322207931 abstract "We develop a new structure of the Green’s function of a second-order elliptic operator in divergence form in a 2D bounded domain. Based on this structure and the theory of rearrangement of functions, we construct concentrated traveling-rotating helical vortex patches to 3D incompressible Euler equations in an infinite pipe. By solving an equation for vorticity $$begin{aligned} w=frac{1}{varepsilon ^2}f_varepsilon left( mathcal {G}_{K_H}w-frac{alpha }{2}|x|^2|ln varepsilon |right) text {in} Omega end{aligned}$$ for small $$ varepsilon >0 $$ and considering a certain maximization problem for the vorticity, where $$ mathcal {G}_{K_H} $$ is the inverse of an elliptic operator $$ mathcal {L}_{K_H} $$ in divergence form, we get the existence of a family of concentrated helical vortex patches, which tend asymptotically to a singular helical vortex filament evolved by the binormal curvature flow. We also get nonlinear orbital stability of the maximizers in the variational problem under $$ L^p $$ perturbation when $$ pge 2. $$" @default.
- W4322207931 created "2023-02-27" @default.
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- W4322207931 date "2023-02-27" @default.
- W4322207931 modified "2023-10-18" @default.
- W4322207931 title "Structure of Green’s function of elliptic equations and helical vortex patches for 3D incompressible Euler equations" @default.
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- W4322207931 doi "https://doi.org/10.1007/s00208-023-02589-8" @default.
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