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Helical vortices with small cross-section for 3D incompressible Euler equation | | Daomin Cao
; Jie Wan
; | | Date: |
1 Jun 2022 | | Abstract: | In this article, we construct traveling-rotating helical vortices with small
cross-section to the 3D incompressible Euler equations in an infinite pipe,
which tend asymptotically to singular helical vortex filament evolved by the
binormal curvature flow. The construction is based on studying a general
semilinear elliptic problem in divergence form egin{equation*} egin{cases}
-varepsilon^2 ext{div}(K(x)
abla u)= (u-q|lnvarepsilon|)^{p}_+, &xin
Omega,\ u=0, &xinpartial Omega, end{cases} end{equation*} for small
values of $ varepsilon. $ Helical vortex solutions concentrating near several
helical filaments with polygonal symmetry are also constructed. | | Source: | arXiv, 2206.00201 | | Services: | Forum | Review | PDF | Favorites | |
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