论文标题
Osgood Vector Fields和2D不可压缩的流体传播奇点
Propagation of singularities by Osgood vector fields and for 2D inviscid incompressible fluids
论文作者
论文摘要
我们表明，某些奇异结构（Hölderian尖端和轻度差异）是由Osgood速度场产生的同构的流动来运输的。这些奇异性的结构与速度连续性的模量有关，结果证明结果很清晰，从某种意义上说，稍微奇异的结构通常无法传播。对于2D Euler方程，我们证明某些奇异结构是由运动保留的，例如$ \ log \ log _+（1/| x |）$ wortices（以及那些单数稍微少一些）的系统以非线性方式传播，直到有限的扰动。我们还为弱的Euler解决方案提供了稳定的结果。
We show that certain singular structures (Hölderian cusps and mild divergences) are transported by the flow of homeomorphisms generated by an Osgood velocity field. The structure of these singularities is related to the modulus of continuity of the velocity and the results are shown to be sharp in the sense that slightly more singular structures cannot generally be propagated. For the 2D Euler equation, we prove that certain singular structures are preserved by the motion, e.g. a system of $\log\log_+(1/|x|)$ vortices (and those that are slightly less singular) travel with the fluid in a nonlinear fashion, up to bounded perturbations. We also give stability results for weak Euler solutions away from their singular set.
