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<p>This paper shows that, in the formal level, the convergence of solutions of Boltzmann equation to solutions of the compressible Navier-Stokes system with small Mach number over the three-dimensional periodic domain <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {T}^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">T</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>, using the relative entropy method originated from Bardos, Golse, Levermore [<i>Comm. Pure Appl. Math.</i> <b>46</b> (1993) 667–753] and Yau [<i>Lett. Math. Phys.</i> <b>22</b> (1991) 63–80]. We discuss the evolution of the entropy which is relative to the local Maxwellian governed by the solution of slightly compressible Navier-Stokes system. This characterizes the convergence rate from Boltzmann equation to the incompressible Navier-Stokes system.</p>

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Relative Entropy and Slightly Compressible Navier-Stokes Dynamics of the Boltzmann Equation

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Yuhan Chen,
  • Ning Jiang

摘要

This paper shows that, in the formal level, the convergence of solutions of Boltzmann equation to solutions of the compressible Navier-Stokes system with small Mach number over the three-dimensional periodic domain \(\mathbb {T}^3\) T 3 , using the relative entropy method originated from Bardos, Golse, Levermore [Comm. Pure Appl. Math. 46 (1993) 667–753] and Yau [Lett. Math. Phys. 22 (1991) 63–80]. We discuss the evolution of the entropy which is relative to the local Maxwellian governed by the solution of slightly compressible Navier-Stokes system. This characterizes the convergence rate from Boltzmann equation to the incompressible Navier-Stokes system.