论文标题
2D不可压缩的Euler方程的Sobolev规律性的瞬时差距丧失
Instantaneous gap loss of Sobolev regularity for the 2D incompressible Euler equations
论文作者
论文摘要
我们在$ \ mathds {r}^2 \ times [0，\ infty）$中构建2D不可压欧方程的解决方案，以便最初的速度位于超临界sobolev sobolev space $ h^β$ $ 1 <β<2 $中，但不在$ h^{β{β{β{β'} $中。 $β'> 1+ \ frac {（3-β）（β-1）} {2 - （β-1）^2} $，$ 0 <t <\ t <\ infty $。这些解决方案不在Yudovich阶级中，但它们在全球范围内存在，它们在坚定的古典解决方案中是独一无二的。
We construct solutions of the 2D incompressible Euler equations in $\mathds{R}^2\times [0,\infty)$ such that initially the velocity is in the super-critical Sobolev space $H^β$ for $1<β<2$, but are not in $H^{β'}$ for $β'>1+\frac{(3-β)(β-1)}{2 - (β-1)^2}$ for $0<t<\infty$. These solutions are not in the Yudovich class, but they exists globally in time and they are unique in a determined family of classical solutions.
