论文标题
在具有可控总能量和交叉螺旋性的MHD系统的弱解决方案上
On the weak solutions for the MHD systems with controllable total energy and cross helicity
论文作者
论文摘要
在本文中，我们证明了$ c（[0，t]; l^2（\ Mathbb {t}^3））$在$ h^{\barβ}（\barβ}（\barβ}（\ MathBb {t} t}^3）$〜（$ habbb）中，$ c {可以在给定的正时间间隔中控制螺旋度。我们的结果将理想MHD系统的非唯一性结果扩展到了粘性和电阻的MHD系统。与理想的MHD系统不同，在\ cite {2beekie}中所做的，粘性和电阻的MHD系统中的耗散效应可防止非线性术语平衡应力错误$（\ rr_q，\ mm_q）$。我们介绍了框流并构建由凸积分方案中的六种不同流动组成的扰动，从而确保迭代有效并产生非唯一性。
In this paper, we prove the non-uniqueness of three-dimensional magneto-hydrodynamic (MHD) system in $C([0,T];L^2(\mathbb{T}^3))$ for any initial data in $H^{\barβ}(\mathbb{T}^3)$~($\barβ>0$), by exhibiting that the total energy and the cross helicity can be controlled in a given positive time interval. Our results extend the non-uniqueness results of the ideal MHD system to the viscous and resistive MHD system. Different from the ideal MHD system, the dissipative effect in the viscous and resistive MHD system prevents the nonlinear term from balancing the stress error $(\RR_q,\MM_q)$ as doing in \cite{2Beekie}. We introduce the box flows and construct the perturbation consisting in six different kinds of flows in convex integral scheme, which ensures that the iteration works and yields the non-uniqueness.
