Titlebook: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids; Yoshikazu Giga,Antonin Novotny Living reference work 2020Latest edition

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Equations for Viscoelastic Fluids, is employed to derive the hydrodynamics of complex fluids which focuses on the competition and coupling between different physical effects. Such a framework also provides guides to the corresponding analysis. This chapter includes those analytical results for both classical solutions with small ini

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Existence and Stability of Viscous Vortices,nt period, evolution is essentially driven by interactions of viscous vortices, the archetype of which is the self-similar Lamb-Oseen vortex. In three dimensions, amplification of vorticity due to stretching can counterbalance viscous dissipation and produce stable tubular vortices. This phenomenon

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Existence and Uniqueness of Strong Stationary Solutions,rt, the compressible Navier–Stokes equations are studied in bounded domains, both for homogeneous (no inflow) and inhomogeneous (inflow) boundary conditions. The solutions are constructed in Sobolev spaces. The next part contains the results for unbounded domains, especially for the exterior domains

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Existence of Stationary Weak Solutions for the Heat Conducting Flows,flux on the boundary proportional to the difference of the temperature inside and outside. In dependence on several parameters, i.e., the adiabatic constant . appearing in the pressure law .(., .) ∼ .. +. and the growth exponent in the heat conductivity, i.e., .(.) ∼ (1 +..), and without any restric

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Finite Time Blowup of Regular Solutions,n the presence of vacuum. It is shown that any smooth solutions to the compressible Navier-Stokes equations for polytropic fluids in the absence of heat conduction will blow up in finite time as long as the initial densities have compact support or isolated mass group. Besides, unified Serrin-type r

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Fourier Analysis Methods for the Compressible Navier-Stokes Equations,es based on Littlewood-Paley decomposition and paradifferential calculus have proved to be very efficient for investigating evolutionary fluid mechanics equations in the whole space or in the torus. The present survey overviews results based on Fourier analysis and paradifferential calculus, for the

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