论文标题
适合3D可压缩欧拉方程的粗糙解决方案的拟合度
Well-posedness for rough solutions of the 3D compressible Euler equations
论文作者
论文摘要
在本文中，我们证明了可压缩3D Euler方程的库奇问题的全部良好性，即本地存在，唯一性和对初始数据的持续依赖性，具有初始速度，密度和涡度$（\ Mathbf {V} _0，ρ_0，ρ_0，ρ_0，ρ_0，\ mathbf {w} w} _0） h^{2+} \ times h^{2} $，在\ cite {wqeuler}的规律性条件下提高。对于可压缩欧拉系统的粗糙解决方案的初始数据的连续依赖是新的，即使具有与\ cite {wqeuler}中相同的规律性条件。此外，我们证明了带有熵的3D可压缩欧拉系统的新局部适应性结果。
In this paper we prove full local well-posedness for the Cauchy problem for the compressible 3D Euler equation, i.e. local existence, uniqueness, and continuous dependence on initial data, with initial velocity, density and vorticity $(\mathbf{v}_0, ρ_0, \mathbf{w}_0) \in H^{2+} \times H^{2+} \times H^{2}$, improving on the regularity conditions of \cite{WQEuler}. The continuous dependence on initial data for rough solutions of the compressible Euler system is new, even with the same regularity conditions as in \cite{WQEuler}. In addition, we prove new local well-posedness results for the 3D compressible Euler system with entropy.
