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This monograph focuses on the partial regularity theorem, as developed by Caffarelli, Kohn, and Nirenberg (CKN), and offers a proof of the upper bound on the Hausdorff dimension of the singular set of weak solutions of the Navier-Stokes inequality, while also providing...
This book offers a thorough guide starting from fundamental functional analysis leading to the coupling of Stokes and Darcy equations, including numerical analysis and scientific computing. Almost all intermediate results are given with complete, rigorous...
This book summarizes the main advances in the field of nonlinear evolution and pattern formation caused by longwave instabilities in fluids. It will allow readers to master the multiscale asymptotic methods and become familiar with applications of these methods in a...
This book is about singular limits of systems of partial differential equations governing the motion of thermally conducting compressible viscous fluids."The main aim is to provide mathematically rigorous arguments how to get from the compressible Navier-Stokes-Fourier...
There are several physico-chemical processes that determine the behavior of multiphase fluid systems – e.g., the fluid dynamics in the different phases and the dynamics of the interface(s), mass transport between the fluids, adsorption effects at the interface, and...
The theory of incompressible multipolar viscous fluids is a non-Newtonian model of fluid flow, which incorporates nonlinear viscosity, as well as higher order velocity gradients, and is based on scientific first principles. The Navier-Stokes model of fluid flow is based...
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