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<p>Given a normalized Maxwellian <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mu =\frac{1}{(2\pi )^{\frac{3}{2}}} e^{-\frac{|v|^2}{2}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>μ</mi> <mo>=</mo> <mfrac> <mn>1</mn> <msup> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>π</mi> <mo stretchy="false">)</mo> </mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </msup> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mrow> <mo stretchy="false">|</mo> <mi>v</mi> <mo stretchy="false">|</mo> </mrow> <mn>2</mn> </msup> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>, we employ a diffusive expansion to derive the Drift–Diffusive–Poisson equations from the Vlasov–Poisson–Fokker–Planck system. We prove the uniform boundedness and time decay estimate for the remainders via a unified nonlinear energy method, and these guarantee the global in time validity of such an expansion up to any order.</p>

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The diffusive limit of Vlasov–Poisson–Fokker–Planck system

  • 期刊论文

  • 发表日期：

    2026年4月4日

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  • Ziwei Huang,
  • Zhengrong Liu

摘要

Given a normalized Maxwellian \(\mu =\frac{1}{(2\pi )^{\frac{3}{2}}} e^{-\frac{|v|^2}{2}}\) μ = 1 ( 2 π ) 3 2 e - | v | 2 2 , we employ a diffusive expansion to derive the Drift–Diffusive–Poisson equations from the Vlasov–Poisson–Fokker–Planck system. We prove the uniform boundedness and time decay estimate for the remainders via a unified nonlinear energy method, and these guarantee the global in time validity of such an expansion up to any order.