涡面问题的朴素参数化
A naive parametrization for the vortex-sheet problem
摘要：
我们考虑由Birkhoff-Rott方程演化的涡面的动力学。流体演化被理解为不可压缩欧拉方程的弱解，其中涡度由曲线上的δ函数乘以振幅给出。我们研究的解具有有限的能量，这意味着零平均振幅。在这种情况下，我们选择一个参数化的涡面运动方程是适定性的分析初始数据。对于振幅方程，我们证明了非解析初始数据的不适定性。
英文摘要：
We consider the dynamics of a vortex sheet that evolves by the Birkhoff-Rott equations. The fluid evolution is understood as a weak solution of the incompressible Euler equations where the vorticity is given by a delta function on a curve multiplied by an amplitude. The solutions we study are with finite energy, which implies zero mean amplitude. In this context we choose a parametrization for the motion of the vortex sheet for which the equation is well-posed for analytic initial data. For the equation of the amplitude we show ill-posedness for non-analytic initial data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
