<p>In the light of recent work in the global well-posedness of solutions for an ionic Vlasov-Poisson system, as demonstrated by Griffin-Pickering and Iacobelli [<CitationRef CitationID="CR1">1</CitationRef>], the current work focuses on the moment propagation of the corresponding system in quasi-neutral regime. Such moment propagation result relies on an estimate of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Q_*(t)=|V(t;0,x,v)-V(0;0,x,v)|\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mi>Q</mi> <mrow> <mrow /> <mo>∗</mo> </mrow> <mrow /> </mmultiscripts> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow> <mo stretchy="false">|</mo> <mi>V</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>;</mo> <mn>0</mn> <mo>,</mo> <mi>x</mi> <mo>,</mo> <mi>v</mi> <mo stretchy="false">)</mo> </mrow> <mo>-</mo> <mi>V</mi> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo>;</mo> <mn>0</mn> <mo>,</mo> <mi>x</mi> <mo>,</mo> <mi>v</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">|</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, where <i>V</i>(<i>s</i>;&#xa0;<i>t</i>,&#xa0;<i>x</i>,&#xa0;<i>v</i>) represents the solution of the characteristic ordinary differential equation associated with the Vlasov-Poisson system. The main goal of this work is to serve the future research on quasi-neutral limit for ionic Vlasov-Poisson system in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {R}^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>.</p>

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Moment propagation of a Vlasov-Poisson system for ion flow in the quasi-neutral regime

  • Zhiwen Zhang

摘要

In the light of recent work in the global well-posedness of solutions for an ionic Vlasov-Poisson system, as demonstrated by Griffin-Pickering and Iacobelli [1], the current work focuses on the moment propagation of the corresponding system in quasi-neutral regime. Such moment propagation result relies on an estimate of \(Q_*(t)=|V(t;0,x,v)-V(0;0,x,v)|\) Q ( t ) = | V ( t ; 0 , x , v ) - V ( 0 ; 0 , x , v ) | , where V(stxv) represents the solution of the characteristic ordinary differential equation associated with the Vlasov-Poisson system. The main goal of this work is to serve the future research on quasi-neutral limit for ionic Vlasov-Poisson system in \(\mathbb {R}^3\) R 3 .