Weighted Spaces with Detached Asymptotics in Application to the Navier-Stokes Equations

Sergueï A. Nazarov ()
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Sergueï A. Nazarov: St. Petersburg University, Math. Mech. Department, Theory of Elasticity

A chapter in Advances in Mathematical Fluid Mechanics, 2000, pp 159-191 from Springer

Abstract: Abstract Function spaces with weighted norms and detached asymptotics naturally appear in the treatment of boundary value problems when linear and nonlinear terms have got same asymptotic behavior 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.

Keywords: Weighted Space; Stokes Problem; Exterior Domain; Weight Index; Angular Part (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-3-642-57308-8_5

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