Annales de l'Institut Henri Poincaré C, Analyse non linéaire ( IF 1.9 ) Pub Date : 2020-07-13 , DOI: 10.1016/j.anihpc.2020.06.006 Dongho Chae 1, 2 , Jörg Wolf 1
In this paper we prove local in time well-posedness for the incompressible Euler equations in for the initial data in , which corresponds to a critical case of the generalized Campanato spaces . The space is studied extensively in our companion paper [9], and in the critical case we have embeddings , where and are the Besov space and the Lipschitz space respectively. In particular contains non- functions as well as linearly growing functions at spatial infinity. We can also construct a class of simple initial velocity belonging to , for which the solution to the Euler equations blows up in finite time.
中文翻译:
广义Campanato空间临界情况下的欧拉方程。
本文证明了不可压缩的Euler方程在时间上的局部适定性 对于中的初始数据 ,它对应于广义Campanato空间的一个临界情况 。在我们的配套论文[9]中对空间进行了广泛的研究,在关键情况下,我们有嵌入方法。,在哪里 和 分别是Besov空间和Lipschitz空间。特别是 包含非空间无穷大处的线性函数和线性增长函数。我们还可以构造一类属于,对此,欧拉方程的解在有限的时间内爆炸了。