论文标题
3D完整可压缩的MHD方程的全球唯一解决方案
Global unique solution for the 3-D full compressible MHD equations in space of lower regularity
论文作者
论文摘要
在本文中，我们为解决方案建立了新的$ l^p $梯度估计，以讨论$ \ mathrm {r}^3 $中的完整可压缩磁性流体动力（MHD）系统的Cauchy问题。我们使用“ $ \ rm {div} - \ rm {curl} $”分解技术（请参阅\ cite {{hjr}，{mr}}），新的修改有效的粘性磁通量和涡流来计算“ $ \ vert \ nabla \ nabla \ nabla \ nabla \ nabla \ mathbf {u} $ {u} $ vert and l^33 33 “ $ \ vert \ nabla \ mathbb {h} \ vert_ {l^3} $”。结果，我们获得了解决方案的全局良好性，而初始数据则在具有较低规律性的一类空间中，而其能量的能量应该很小。
In this paper, we establish new $L^p$ gradient estimates of the solutions in order to discuss Cauchy problem for the full compressible magnetohydrodynamic(MHD) systems in $\mathrm{R}^3$. We use the "$\rm{div}-\rm{curl}$" decomposition technique (see \cite{{HJR},{MR}}) and new modified effective viscous flux and vorticity to calculate "$\Vert\nabla \mathbf{u}\Vert_{L^3}$" and "$\Vert\nabla \mathbb{H}\Vert_{L^3}$".As a result, we obtain global well-posedness for the solution with the initial data being in a class of space with lower regularity, while the energy of which should be suitably small.
