论文标题
根据相关压力，针对MHD方程弱解决方案的新规则性标准
New Regularity Criteria for Weak Solutions to the MHD Equations in Terms of an Associated Pressure
论文作者
论文摘要
我们证明，如果$ 0 <t_0 <t \ leq \ infty $，$（\ mathbf {u}，\ mathbf {b}，p），p）$是MHD方程的合适解决方案，则$ \ Mathbb {r}^3 \ times（0，t）$ \ mathbb {r} l^{\ infty}（0，t_0; \，l^{3/2}（\ Mathbb {r}^3））$或$ \ m nathcal {f}_γ（（（（| \ Mathbf {U} | l^{\ infty}（0，t_0; \，l^{3/2}（\ Mathbb {r}^3））$对于某些$γ> 0 $，其中$ \ nathcal {f}_γ（s）= s \ s = s \ s = s \，[分别表示负极和非负部分，然后说明解决方案$（\ Mathbf {u}，\ Mathbf {B}，P），P）$在$ \ Mathbb {r}^3 \ times（0，T_0] $中没有单数点。
We prove that if $0<T_0<T\leq\infty$, $(\mathbf{u},\mathbf{b},p)$ is a suitable weak solution of the MHD equations in $\mathbb{R}^3\times(0,T)$ and either $\mathcal{F}_γ(p_-)\in L^{\infty}(0,T_0;\, L^{3/2}(\mathbb{R}^3))$ or $\mathcal{F}_γ((|\mathbf{u}|^2+ |\mathbf{b}|^2+2p)_+)\in L^{\infty}(0,T_0;\, L^{3/2}(\mathbb{R}^3))$ for some $γ>0$, where $\mathcal{F}_γ(s)=s\, [\ln{}(1+ s)]^{1+γ}$ and the subscripts "$-$" and "$+$" denote the negative and the nonnegative part, respectively, then the solution $(\mathbf{u},\mathbf{b},p)$ has no singular points in $\mathbb{R}^3\times(0,T_0]$.
