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Weighted spaces with detached asymptotics in application to the Navier-Stokes equations. (English) Zbl 0974.35088
Málek, Josef (ed.) et al., Advances in mathematical fluid mechanics. Lecture notes of the 6th international school on mathematical theory in fluid mechanics, Paseky, Czech Republic, September 19-26, 1999. Berlin: Springer. 159-191 (2000).
From the author’s abstract: Function spaces with weighted norms and detached asymptotics naturally appear in the treatment of boundary-value problems when linear and nonlinear terms have the same asymptotic behaviour either at a singularity point of the boundary, or at infinity. The characteristic feature of these spaces is that their norms are composed from both, norms of angular parts in the detached terms and norms of asymptotic remainders. The developed approach is described for the Navier-Stokes problems in domains with conical (angular) outlets to infinity while the 3-D exterior and 2-D aperture problems imply representative examples. With a view towards compressible and non-Newtonian fluids, the described technique is applied to the transport equation as well.
For the entire collection see [Zbl 0949.00020].

35Q30 Navier-Stokes equations
46N20 Applications of functional analysis to differential and integral equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids