论文标题
具有指数或亚指数总和的矢量场的经典流量
Classical flows of vector fields with exponential or sub-exponential summability
论文作者
论文摘要
我们表明，矢量字段$ b $的空间衍生物$ d_xb $满足Orlicz的总结条件具有空间连续的代表，并且已妥善。对于亚指数总结性的情况，它们的流量也以定量形式满足了lusin（n）条件。此外，我们证明，如果$ d_xb $满足合适的指数总和条件，那么与$ b $相关的流量具有SOBOLEV的规律性，而无需假设$ {\ rm div} _xb $的有限性。然后，我们将这些结果应用于Cauchy问题的弱解决方案的表示和连续性方程的弱解决方案。
We show that vector fields $b$ whose spatial derivative $D_xb$ satisfies a Orlicz summability condition have a spatially continuous representative and are well-posed. For the case of sub-exponential summability, their flows satisfy a Lusin (N) condition in a quantitative form, too. Furthermore, we prove that if $D_xb$ satisfies a suitable exponential summability condition then the flow associated to $b$ has Sobolev regularity, without assuming boundedness of ${\rm div}_xb$. We then apply these results to the representation and Sobolev regularity of weak solutions of the Cauchy problem for the transport and continuity equations.
