论文标题
具有动态涡度的二维压缩EULER方程的低规律性解决方案
Low regularity solutions of two-dimensional compressible Euler equations with dynamic vorticity
论文作者
论文摘要
通过对速度和密度建立尖锐的Strichartz估计值，我们证明了解决方案的局部解决方案的局部解决方案，对于二维可压缩的Euler方程，最初的速度，密度和特定的涡度$（\ bv_0，ρ_0，ρ_0，\ varpi_0） h^{s}（\ Mathbb {r}^2）\ times h^{s}（\ mathbb {r}^2）\ times h^2（\ Mathbb {r}^2），s> \ frac {7} {4} {4} {4} $。我们的策略依赖于Smith-Tataru的工作\ cite {st}对于准线性波方程。
By establishing a sharp Strichartz estimate for the velocity and density, we prove the local well-posedness of solutions for the Cauchy problem of two-dimensional compressible Euler equations, where the initial velocity, density, and specific vorticity $(\bv_0, ρ_0, \varpi_0) \in H^{s}(\mathbb{R}^2)\times H^{s}(\mathbb{R}^2) \times H^2(\mathbb{R}^2), s>\frac{7}{4}$. Our strategy relies on Smith-Tataru's work \cite{ST} for quasi-linear wave equations.
