Existence of global weak solutions to a hybrid Vlasov‐MHD model for magnetized plasmas

机译：对磁化等离子体混合vlasov-MHD模型的全局弱解的存在

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Abstract >We prove the global‐in‐time existence of large‐data finite‐energy weak solutions to an incompressible hybrid Vlasov‐magnetohydrodynamic model in three space dimensions. The model couples three essential ingredients of magnetized plasmas: a transport equation for the probability density function, which models energetic rarefied particles of one species; the incompressible Navier–Stokes system for the bulk fluid; and a parabolic evolution equation, involving magnetic diffusivity, for the magnetic field. The physical derivation of our model is given. It is also shown that the weak solution, whose existence is established, has nonincreasing total energy, and that it satisfies a number of physically relevant properties, including conservation of the total momentum, conservation of the total mass, and nonnegativity of the probability density function for the energetic particles. The proof is based on a one‐level approximation scheme, which is carefully devised to avoid increase of the total energy for the sequence of approximating solutions, in conjunction with a weak compactness argument for the sequence of approximating solutions. The key technical challenges in the analysis of the mathematical model are the nondissipative nature of the Vlasov‐type particle equation and passage to the weak limits in the multilinear coupling terms. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><abstract xmlns =“http://www.wiley.com/namespaces/wiley”type =“main”> <title type =“main”>抽象</ title> >我们证明了全局时间内存三个空间尺寸的不可压缩混合Vlasov-磁流力学模型的大数据有限能量弱解。该模型耦合三种磁化等离子体的必需成分：概率密度函数的传输方程，其中一种物种精力稀有的颗粒;用于散装液的不可压缩的Navier-Stokes系统;和磁场涉及磁扩散性的抛物线演化方程。给出了我们模型的物理推导。还表明，建立存在的弱溶液具有不可释放的总能量，并且它满足了许多物理相关的性质，包括节约总动量，节约总质量，并且概率密度函数的非空间性。对于能量粒子。证据基于一个级别的近似方案，仔细设计，以避免近似解的序列序列的总能量的增加，以及近似解的序列的弱紧凑性参数。数学模型分析中的关键技术挑战是VLASOV型粒子方程的不良性和多线耦合术语中的弱极限的通道。</ p> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-29812/'>《Proceedings of the London Mathematical Society》</a> <b style="margin: 0 2px;">|</b><span>2017年第4期</span><b style="margin: 0 2px;">|</b><span>共43页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Cheng Bin&option=202" target="_blank" rel="nofollow">Cheng Bin;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Süli Endre&option=202" target="_blank" rel="nofollow">Süli Endre;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Tronci Cesare&option=202" target="_blank" rel="nofollow">Tronci Cesare;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Department of MathematicsUniversity of SurreyGuildford GU2 7XH United Kingdom;</p> <p>Mathematical InstituteUniversity of OxfordWoodstock Road Oxford OX2 6GG United Kingdom;</p> <p>Department of MathematicsUniversity of SurreyGuildford GU2 7XH United Kingdom;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/156.html" title="数学">数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=35D30&option=203" rel="nofollow">35D30;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=35Q83&option=203" rel="nofollow">35Q83;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=76W05 (primary)&option=203" rel="nofollow">76W05 (primary);</a> </p> <div class="translation"> 机译：35D30;35Q83;76W05（初级）; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704024593411.html">Existence of global weak solutions to a hybrid Vlasov‐MHD 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