This paper studies the very weak solution to the steady MHD type system in a bounded domain. We prove the existence of very weak solutions to the MHD type system for arbitrary large external forces $ ({\bf f},{\bf{g}}) $ in $ L^r({\Omega})\times [X_{\theta',q'}({\Omega})]' $ and suitable boundary data $ ({\mathcal B}^0,{\mathcal U}^0) $ in $ W^{-1/p,p}({\partial}{\Omega})\times W^{-1/q,q}({\partial}{\Omega}) $, under certain assumptions on $ p,q,r,\theta $. The uniqueness of very weak solution for small data $ ({\bf f},{\bf{g}},{\mathcal B}^0,{\mathcal U}^0) $ is also studied.

中文翻译：

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MHD型系统极弱解的存在性和唯一性

本文研究了有限域中稳定MHD类型系统的非常弱的解。我们证明了对于任意大的外力$（{\ bf f}，{\ bf {g}}）$ in L ^ r（{\ Omega}）\ times [X_ {\ theta'，q'}（{\ Omega}）]'$和合适的边界数据$（{\ mathcal B} ^ 0，{\ mathcal U} ^ 0）$ in $ W ^ {-1 / p， p}（{\ partial} {\ Omega}）\ times W ^ {-1 / q，q}（{\ partial} {\ Omega}）$，在$ p，q，r，\ theta $的某些假设下。还研究了小数据$（{\ bf f}，{\ bf {g}}，{\ mathcal B} ^ 0，{\ mathcal U} ^ 0）$的非常弱的解的唯一性。