Scholarlink

<p>We broaden the application of the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(l^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>l</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-decoupling theorem to the Boltzmann equation. We prove Strichartz estimates for the linear problem in the <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathbb {T}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">T</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation> setting. We establish space-time bilinear estimates, and hence the unconditional uniqueness of solutions to the <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathbb {R}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\mathbb {T}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">T</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation> Boltzmann equation for the Maxwellian particle and soft potential with an angular cutoff, adopting a unified hierarchy scheme originally developed for the nonlinear Schrödinger equation.</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

\(l^{2}\)-Decoupling and the Unconditional Uniqueness for the Boltzmann Equation

  • 期刊论文

  • 发表日期：

    2026年5月2日

查看全文
  • Xuwen Chen,
  • Shunlin Shen,
  • Zhifei Zhang

摘要

We broaden the application of the \(l^{2}\) l 2 -decoupling theorem to the Boltzmann equation. We prove Strichartz estimates for the linear problem in the \(\mathbb {T}^d\) T d setting. We establish space-time bilinear estimates, and hence the unconditional uniqueness of solutions to the \(\mathbb {R}^d\) R d and \(\mathbb {T}^d\) T d Boltzmann equation for the Maxwellian particle and soft potential with an angular cutoff, adopting a unified hierarchy scheme originally developed for the nonlinear Schrödinger equation.