论文标题
分段光滑的平稳静态欧拉流通过过度确定的边界问题与紧凑的支撑
Piecewise smooth stationary Euler flows with compact support via overdetermined boundary problems
论文作者
论文摘要
我们在紧凑的支持下构建了3D Euler方程的新固定弱解。溶液在表面上平滑且不连续，轴对称为旋转。我们发现的溶液范围与Gavrilov和Constantin-La-Vicol最近获得的平滑固定溶液家族不同，并且大于且大。特别是，这些解决方案不可本地化。证明的关键步骤是构建解决过度确定的椭圆边界价值问题的解决方案，其中既有dirichlet和neumann数据。
We construct new stationary weak solutions of the 3D Euler equation with compact support. The solutions, which are piecewise smooth and discontinuous across a surface, are axisymmetric with swirl. The range of solutions we find is different from, and larger than, the family of smooth stationary solutions recently obtained by Gavrilov and Constantin-La-Vicol; in particular, these solutions are not localizable. A key step in the proof is the construction of solutions to an overdetermined elliptic boundary value problem where one prescribes both Dirichlet and (nonconstant) Neumann data.
