03198nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002900185100003000214245017900244260008200423300003400505336002600539337002600565338003600591347002400627490005300651506006600704520177500770650002802545650002502573650004002598650005202638700003502690856003202725856006702757239-190314CH-001817-320190314233005.0a fot ||| 0|cr nn mmmmamaa190314e20190331sz fot ||| 0|eng d a978303719693970a10.4171/1932doi ach0018173 7aPHDF2bicssc a76-xxa35-xxa82-xx2msc1 aArsénio, Diogo,eauthor.10aFrom the Vlasov–Maxwell–Boltzmann System to Incompressible Viscous Electro-magneto-hydrodynamicsh[electronic resource] :bVolume 1 /cDiogo Arsénio, Laure Saint-Raymond3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2019 a1 online resource (418 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe Vlasov–Maxwell–Boltzmann system is a microscopic model to describe the dynamics of charged particles subject to self-induced electromagnetic forces. At the macroscopic scale, in the incompressible viscous fluid limit the evolution of the plasma is governed by equations of Navier–Stokes–Fourier type, with some electromagnetic forcing that may take on various forms depending on the number of species and on the strength of the interactions.
From the mathematical point of view, these models have very different behaviors. Their analysis therefore requires various mathematical methods which this book aims to present in a systematic, painstaking, and exhaustive way.
The first part of this work is devoted to the systematic formal analysis of viscous hydrodynamic limits of the Vlasov–Maxwell–Boltzmann system, leading to a precise classification of physically relevant models for viscous incompressible plasmas, some of which have not previously been described in the literature.
In the second part, the convergence results are made precise and rigorous, assuming the existence of renormalized solutions for the Vlasov–Maxwell–Boltzmann system. The analysis is based essentially on the scaled entropy inequality. Important mathematical tools are introduced, with new developments used to prove these convergence results (Chapman–Enskog-type decomposition and regularity in the $v$ variable, hypoelliptic transfer of compactness, analysis of high frequency time oscillations, and more).
The third and fourth parts (which will be published in a second volume) show how to adapt the arguments presented in the conditional case to deal with a weaker notion of solutions to the Vlasov–Maxwell–Boltzmann system, the existence of which is known.07aFluid mechanics2bicssc07aFluid mechanics2msc07aPartial differential equations2msc07aStatistical mechanics, structure of matter2msc1 aSaint-Raymond, Laure,eauthor.40uhttps://doi.org/10.4171/193423cover imageuhttps://www.ems-ph.org/img/books/arsenio_mini.jpg