论文标题
低规律性的非$ l^2（r^n）$ gmhd-alpha系统的本地解决方案
Low regularity of non-$L^2(R^n)$ local solutions to gMHD-alpha systems
论文作者
论文摘要
方程式的磁液动力学（MHD）系统控制粘性流体受磁场的影响，并通过Navier-Stokes方程和Maxwell方程的耦合得出。最近，研究基于流体的微分方程的概括已成为常见。在这里，我们考虑了广义的磁性流动力α（GMHD- $α$）系统，该系统与原始MHD系统不同，它通过包括附加的非线性术语（由$α$索引），并用更通用的傅立叶型乘数替换了Laplace运营商，由$ - | exc./ g（|）$ - | exg（| | | | | | | | | | | | |）在Pennington的论文中，在Sobolev Space $ H^{s，2}（\ Mathbb {r}^n）$的初始数据中考虑了问题。在这里，我们考虑了$ h^{s，p}中的初始数据的问题（\ mathbb {r}^n）$，$ n \ geq 3 $和$ p> 2 $。我们的目标是最大程度地减少获得解决方案独特性所需的规律性。
The Magneto-Hydrodynamic (MHD) system of equations governs viscous fluids subject to a magnetic field and is derived via a coupling of the Navier-Stokes equations and Maxwell's equations. Recently it has become common to study generalizations of fluids-based differential equations. Here we consider the generalized Magneto-Hydrodynamic alpha (gMHD-$α$) system, which differs from the original MHD system by including an additional non-linear terms (indexed by $α$), and replacing the Laplace operators by more general Fourier multipliers with symbols of the form $-|ξ|^γ/ g(|ξ|)$. In a paper by Pennington, the problem was considered with initial data in the Sobolev space $H^{s,2}(\mathbb{R}^n)$ with $n \geq 3$. Here we consider the problem with initial data in $H^{s,p}(\mathbb{R}^n)$ with $n \geq 3$ and $p > 2$. Our goal is to minimize the regularity required for obtaining uniqueness of a solution.
