Nonlinear Conservation Laws and Applications

0369769 - MÚ 2012 RIV US eng M - Monography Chapter
Feireisl, Eduard
Mathematical analysis of fluid in motion.
Nonlinear Conservation Laws and Applications. 1st ed. New York: Springer, 2011 - (Bressan, A.), s. 73-100. The IMA Volumes in Mathematics and its Applications, 153. ISBN 978-1-4419-9553-7
R&D Projects: GA ČR GA201/08/0315
Institutional research plan: CEZ:AV0Z10190503
Keywords : Navier-Stokes system * fluid mechanics * scale analysis
Subject RIV: BA - General Mathematics
http://www.springerlink.com/content/978-1-4419-9554-4

Continuum fluid mechanics is a phenomenological theory based on macroscopic observable state variables, the time evolution of which is described by means of systems of partial differential equations. The resulting mathematical problems are highly non-linear and rather complex, even in the simplest physically relevant situations. We discuss several recent results and newly developed methods based on the concept of weak solution. The class of weak solutions is happily large enough in order to guarantee the existence of global-in-time solutions without any essential restrictions on the size of the relevant data. On the other hand, the underlying structural hypotheses impose quite severe restrictions on the specific form of constitutive relations. The best known open problems - hypothetical presence of vacuum zones, propagation of density oscillations, sequential stability of the temperature field, among others - are discussed.
Permanent Link: http://hdl.handle.net/11104/0203761