Scholarlink

<p>We are concerned with the estimate of singular set of weak solution to Magneto-hydrodynamical (MHD) equations. First, we show that if the pressure <i>P</i> associated to a Leray-Hopf weak solution (<i>u</i>,&#xa0;<i>b</i>) satisfies some additional assumptions, then there is a reduction in the Hausdorff dimension of singular set at a first potential blow up time. Next, instead of imposing the assumption on the pressure, we prove that if the initial data satisfies an extra assumption, then (<i>u</i>,&#xa0;<i>b</i>) possess finite number singular points at first potential blow up time.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The Estimate of Singular Set of Weak Solution to MHD Equations

  • 期刊论文

  • 发表日期：

    2026年4月13日

查看全文
  • Zhong Tan,
  • Jianfeng Zhou

摘要

We are concerned with the estimate of singular set of weak solution to Magneto-hydrodynamical (MHD) equations. First, we show that if the pressure P associated to a Leray-Hopf weak solution (u, b) satisfies some additional assumptions, then there is a reduction in the Hausdorff dimension of singular set at a first potential blow up time. Next, instead of imposing the assumption on the pressure, we prove that if the initial data satisfies an extra assumption, then (u, b) possess finite number singular points at first potential blow up time.