Scholarlink

<p>In the present paper, we consider the well-posedness of 3D MHD equations with the damping terms <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10253_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="57" /> </InlineMediaObject> <EquationSource Format="TEX">\(|u|^{\alpha -1}u\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mo stretchy="false">|</mo> <mi>u</mi> <mo stretchy="false">|</mo> </mrow> <mrow> <mi>α</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>u</mi> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10253_Article_IEq2.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">\(|B|^{\beta -1}B\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mo stretchy="false">|</mo> <mi>B</mi> <mo stretchy="false">|</mo> </mrow> <mrow> <mi>β</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>B</mi> </mrow> </math></EquationSource> </InlineEquation> (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10253_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="61" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha ,\beta \ge 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>) defined on time-varying domains with homogeneous Dirichlet boundary conditions. We show that the damped 3D MHD system has global weak solutions for any <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10253_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="92" /> </InlineMediaObject> <EquationSource Format="TEX">\(1\le \alpha ,\beta \le 5\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>≤</mo> <mn>5</mn> </mrow> </math></EquationSource> </InlineEquation> and the weak solution is unique for any <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10253_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="92" /> </InlineMediaObject> <EquationSource Format="TEX">\(4\le \alpha ,\beta \le 5\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>4</mn> <mo>≤</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>≤</mo> <mn>5</mn> </mrow> </math></EquationSource> </InlineEquation>.</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

Well-Posedness of 3D MHD Equations with Damping on Time-Varying Domains

  • 期刊论文

  • 发表日期：

    2025年4月2日

查看全文
  • Xiaoya Song

摘要

In the present paper, we consider the well-posedness of 3D MHD equations with the damping terms \(|u|^{\alpha -1}u\) | u | α - 1 u and \(|B|^{\beta -1}B\) | B | β - 1 B ( \(\alpha ,\beta \ge 1\) α , β ≥ 1 ) defined on time-varying domains with homogeneous Dirichlet boundary conditions. We show that the damped 3D MHD system has global weak solutions for any \(1\le \alpha ,\beta \le 5\) 1 ≤ α , β ≤ 5 and the weak solution is unique for any \(4\le \alpha ,\beta \le 5\) 4 ≤ α , β ≤ 5 .