论文标题
耗时欧拉流量用于涡流表的初始数据，而没有区别符号
Dissipative Euler flows for vortex sheet initial data without distinguished sign
论文作者
论文摘要
我们为2D不可压缩的Euler方程构建了无限的弱解决方案，以构建涡流板初始数据。我们的初始基准的涡度集中在合适的Hölder空间中的简单封闭曲线上，并且涡度可能没有区别的符号。我们的解决方案是通过凸集成获得的。它们在“湍流”区域外平滑，该区域在涡流纸周围及时线性生长。作为副产品，该方法显示了湍流区的生长如何受局部能量不平等的控制，并根据涡流板强度来测量最大的初始耗散率。
We construct infinitely many admissible weak solutions to the 2D incompressible Euler equations for vortex sheet initial data. Our initial datum has vorticity concentrated on a simple closed curve in a suitable Hölder space and the vorticity may not have a distinguished sign. Our solutions are obtained by means of convex integration; they are smooth outside a "turbulence" zone which grows linearly in time around the vortex sheet. As a byproduct, this approach shows how the growth of the turbulence zone is controlled by the local energy inequality and measures the maximal initial dissipation rate in terms of the vortex sheet strength.
