Constantin, P., Debussche, A., Galdi, G.P., Růžička, M., Seregin, G.
Flandoli, Franco, Beirão da Veiga, Hugo (Eds.)
2013, IX, 313 p.
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The range of theoretical fluid-mechanics problems treated here is unique in its kind
The lectures are updated versions of contemporary knowledge in the field
It is an outstanding introduction to research on fluids for young scientists
This volume brings together five contributions to mathematical fluid mechanics, a classical but still very active research field which overlaps with physics and engineering. The contributions cover not only the classical Navier-Stokes equations for an incompressible Newtonian fluid, but also generalized Newtonian fluids, fluids interacting with particles and with solids, and stochastic models. The questions addressed in the lectures range from the basic problems of existence of weak and more regular solutions, the local regularity theory and analysis of potential singularities, qualitative and quantitative results about the behavior in special cases, asymptotic behavior, statistical properties and ergodicity.
Fluids and Particles.- Stochastic Navier-Stokes Equations: well Posedness and Ergodic Properties.- Topics in the Mathematical Theory of Fluid-Solid Interaction.- Analysis of Generalized Newtonian Fluids.- Local Regularity Theory for the Navier-Stokes Equations.