论文标题
2D可压缩欧拉方程和理想MHD系统的Cauchy问题在$ H^\ frac {7} {4} {4}（\ Mathbb {r}^2）中
The Cauchy problems for the 2D compressible Euler equations and ideal MHD system are ill-posed in $H^\frac{7}{4}(\mathbb{R}^2)$
论文作者
论文摘要
在分数sobolev空间中，$ h^\ frac {7} {4}（\ mathbb {r}^2）$，我们证明了2D可压缩的欧拉方程和2D理想可压缩的MHD系统所需的低调性不适当结果。对于Euler方程，相对于流体速度和密度的规律性，它是锋利的。所获得的未拟合性的机制是瞬时冲击形成。
In a fractional Sobolev space $H^\frac{7}{4}(\mathbb{R}^2)$, we prove the desired low-regularity ill-posedness results for the 2D compressible Euler equations and the 2D ideal compressible MHD system. For the Euler equations, it is sharp with respect to the regularity of the fluid velocity and density. The mechanism behind the obtained ill-posedness is the instantaneous shock formation.
