Advances In Mathematical Fluid Mechanics
This book consists of six survey contributions, focusing on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids. The following topics are studied intensively within the book: global in time qualitative properties of solutions to compressible fluid models; fluid mechanics limits, as compressible-incompressible, kinetic-macroscopic, viscous-inviscid; adaptive Navier-Stokes solver via wavelets; well-posedness of the evolutionary Navier-Stokes...
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This book consists of six survey contributions, focusing on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids. The following topics are studied intensively within the book: global in time qualitative properties of solutions to compressible fluid models; fluid mechanics limits, as compressible-incompressible, kinetic-macroscopic, viscous-inviscid; adaptive Navier-Stokes solver via wavelets; well-posedness of the evolutionary Navier-Stokes equations in 3D; existence theory for the incompressible Navier-Stokes equations in exterior and aperture domains. All six articles present significant results and provide a better understanding of the problems in areas that enjoy long-lasting attention of researchers dealing with fluid mechanics PDEs. Although the papers have the character of detailed summaries, their central parts contain the newest results achieved by the authors who are experts in the topics they present.
Viscous Flows in Besov Spaces1The Dynamical Systems Approach to the Navier-Stokes Equations of Compressible Fluids35Adaptive Wavelet Solvers for the Unsteady Incompressible Navier-Stokes Equations67Asymptotic Problems and Compressible-Incompressible Limit119Weighted Spaces with Detached Asymptotics in Application to the Navier-Stokes Equations159On the Mathematical Theory of Fluid Dynamic Limits to Conservation Laws192
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