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تسجيل مستخدم جديدExistence of stationary vortex sheets for the 2D Euler equation
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We investigate a steady planar flow of an ideal fluid in a (bounded or unbounded) domain $Omegasubset mathbb{R}^2$. Let $kappa_i ot=0$, $i=1,ldots, m$, be $m$ arbitrary fixed constants. For any given non-degenerate critical point $mathbf{x}_0=(x_{0,1},ldots,x_{0,m})$ of the Kirchhoff-Routh function defined on $Omega^m$ corresponding to $(kappa_1,ldots, kappa_m)$, we construct a family of stationary planar flows with vortex sheets that have large vorticity amplitude and are perturbations of small circles centered near $x_i$, $i=1,ldots,m$. The proof is accomplished via the implicit function theorem with suitable choice of function spaces. This seems to be the first nontrivial result on the existence of stationary vortex sheets in domains.
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