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Hu, Xianpeng (2010) WEAK SOLUTIONS AND INCOMPRESSIBLE LIMITS OFMULTI-DIMENSIONAL MAGNETOHYDRODYNAMIC FLOWS. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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This dissertation addresses mathematical issues regarding the existence of global weak so-lutions of isentropic compressible magnetohydrodynamic flows (MHD), the limit behaviorof isentropic compressible MHD as Mach number vanishes, and the hydrodynamic limit ofVlasov-Maxwell-Boltzemann equations. More precisely, in the first part, global existenceof weak solutions with large initial data to the Cauchy problem of the three-dimensionalcompressible MHD is established through an invading method for the adiabatic exponent&Gamma > 3/2 and constant viscosity coefficients. In the second part, we focus on the connectionbetween the incompressible MHD and the compressible isentropic MHD; it is showed that asMach number vanishes, the compressible isentropic MHD will converge to the incompress-ible MHD. In the third part, using relative entropy estimate about an absolute Maxwellian,we establish an incompressible Electron-Magnetohydrodynamics-Fourier limit for solutionsof the Vlasov-Maxwell-Blotzmann equation considered over any periodic spatial domain inR^3. It is shown that any properly scaled sequence of renormalized solutions of Vlasov-Maxwell-Boltzmann equations has fluctuations that (in the weak L2 topology) converge toan in¯nitesimal Maxwellian with fluid variables that satisfy the incompressibility and Boussi-nesq relations. It is shown that every limit point and the magnetic field are governed by aweak solution of an incompressible electron-magnetohydrodynamics system for all time.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Hu, Xianpengxih15@pitt.eduXIH15
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairWang, Dehuadwang@math.pitt.eduDHWANG
Committee MemberGaldi, Giovanni Pgaldi@engr.pitt.eduGALDI
Committee MemberJiang, Huiqianghqjiang@pitt.eduHQJIANG
Committee MemberHastings, Stuart Psph@math.pitt.eduSPH
Committee MemberLayton, William Jwjl@pitt.eduWJL
Date: 30 September 2010
Date Type: Completion
Defense Date: 6 April 2010
Approval Date: 30 September 2010
Submission Date: 14 July 2010
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Cauchy problem; Global weak solutions; Incompress-; Renormalized solutions
Other ID:, etd-07142010-090003
Date Deposited: 10 Nov 2011 19:51
Last Modified: 15 Nov 2016 13:45


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