论文标题
用$ h^β$ $β> 0 $的初始数据构建3D Euler方程的解决方案
Construction of solutions to the 3D Euler equations with initial data in $H^β$ for $β>0$
论文作者
论文摘要
在本文中，我们使用凸集成的方法来构建$ h^β$以$ 0 <β\ ll1 $的无限分布解决方案，以构建三维不可压缩的Euler方程的初始值问题。我们表明，如果初始数据在$ l^2 $中具有任何小的分数衍生物，那么我们可以使用一些规律性构建解决方案，因此相应的$ l^2 $能量是及时的。这与E. Wiedemann，Ann的$ L^2 $存在。研究HenriPoincaré，肛门。 Noninéaire28，第5、727--730号（2011; ZBL 1228.35172），其中能量不连续$ 0 $。
In this paper, we use the method of convex integration to construct infinitely many distributional solutions in $H^β$ for $0<β\ll1$ to the initial value problem for the three-dimensional incompressible Euler equations. We show that if the initial data has any small fractional derivative in $L^2$, then we can construct solutions with some regularity, so that the corresponding $L^2$ energy is continuous in time. This is distinct from the $L^2$ existence result of E. Wiedemann, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 28, No. 5, 727--730 (2011; Zbl 1228.35172), where the energy is discontinuous at $0$.
