Asymptotic behavior of global smooth solutions for bipolar compressible Navier-Stokes-Maxwell system from plasmas. Issue 5 (September 2015)

• Record Type: Journal Article
• Authors: FENG, Yuehong; WANG, Shu; LI, Xin
• Is Part Of: Acta mathematica scientia. Volume 35:Issue 5(2015)
• Page Start: 955
• Page End: 969
• Publication Date: 2015-09
• Subjects: Mathematical physics -- Periodicals; 530.15
• DOI: 10.1016/S0252-9602(15)30030-8
• Languages: English
• ISSNs: 0252-9602

Abstract

<abstract abstract-type="author" id="ceab10"> <title id="cestitle10">Abstract</title> <sec> <p id="spara10">This paper is concerned with the bipolar compressible Navier-Stokes-Maxwell system for plasmas. We investigated, by means of the techniques of symmetrizer and elaborate energy method, the Cauchy problem in <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj28jbmfw6" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si1.gif" overflow="scroll" id="d13e137" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>ℝ</mml:mi><mml:mn>3</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>. Under the assumption that the initial values are close to a equilibrium solutions, we prove that the smooth solutions of this problem converge to a steady state as the time goes to the infinity. It is shown that the difference of densities of two carriers converge to the equilibrium states with the norm <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj28jbmg31" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si2.gif" overflow="scroll" id="d13e145" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mo>‖</mml:mo><mml:mo>.</mml:mo><mml:mo>‖</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mrow><mml:mtext>s</mml:mtext><mml:mo>-</mml:mo><mml:mtext>1</mml:mtext></mml:mrow></mml:msup></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>, while the velocities and the electromagnetic fields converge to the equilibrium states with weaker norms than <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgj28jbmg31" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="si2.gif" overflow="scroll" id="d13e168" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mo>‖</mml:mo><mml:mo>.</mml:mo><mml:mo>‖</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msup><mml:mi>H</mml:mi><mml:mrow><mml:mtext>s</mml:mtext><mml:mo>-</mml:mo><mml:mtext>1</mml:mtext></mml:mrow></mml:msup></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>. This phenomenon on the charge transport shows the essential difference between the unipolar Navier-Stokes-Maxwell and the bipolar Navier-Stokes-Maxwell system.</p> </sec> </abstract>