| Abstract: |
| In this talk, we consider the existence of traveling-rotating helical vortices to 3D incompressible Euler equations in infinite cylinders, whose support sets consist of helical tubes with small cross-sections of radius $ O(\varepsilon) $ and concentrate near several types of co-rotating helical solutions of nearly parallel vortex filaments model as $ \varepsilon\to 0 $, which justify the result in Klein, Majda and Damodaran [1995, JFM] and generalize results in Guerra and Musso [2026, Math Ann]. The key is to find clustered solutions to a semilinear elliptic equations in divergence form
\begin{equation*}
\begin{cases}
-\varepsilon^2\text{div}(K(x)\nabla u)= (u-q|\ln\varepsilon|)^{p}_+,\ \ &x\in \Omega,\
u=0,\ \ &x\in\partial \Omega
\end{cases}
\end{equation*}
for small values of $ \varepsilon $. This is a joint work with Prof. Daomin Cao. |
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