Titlebook: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids; Yoshikazu Giga,Antonín Novotný Reference work 2018 Springer Internationa

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Self-Similar Solutions to the Nonstationary Navier-Stokes Equationsm special solutions which are scale invariant with respect to the natural scaling. These solutions are often called self-similar solutions. In this chapter, important results for both forward self-similar and backward self-similar solutions are reviewed, and open problems will be mentioned.

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Time-Periodic Solutions to the Navier-Stokes Equationsm models the flow of a viscous liquid under the influence of a time-periodic force. The three most relevant types of flow domains, from a physical point of view, are considered: a bounded domain, an exterior domain, and an infinite pipe. Methods to show existence of both weak and strong solutions ar

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Critical Function Spaces for the Well-Posedness of the Navier-Stokes Initial Value Problemof the equations. More specifically the initial value problem is studied in scale-invariant function spaces, insisting on the special role of the “largest” scale-invariant function space; the specificity of two space dimensions is recalled, in terms of the velocity field and the vorticity. Some exam

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Existence and Stability of Viscous Vorticesnt 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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Models and Special Solutions of the Navier-Stokes Equations are classical examples, but they are looked at from a modern viewpoint of partial differential equations. Also considered are model equations describing motion of incompressible viscous fluid. Demonstrations are given for importance of both nonlinearity and nonlocality alike by mathematical analyse

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The Inviscid Limit and Boundary Layers for Navier-Stokes Flowse to solutions of the Euler equations modeling inviscid incompressible flows as viscosity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics. The problem is classified into two categories: the case when the physical boundary is absent, and the case when the physic

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