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On NAVIER-STOKES and KELVIN-VOIGT Equations in Three Dimensions in Interpolation Spaces

✍ Scribed by Michael Böhm

Publisher: John Wiley and Sons
Year: 1992
Tongue: English
Weight: 650 KB
Volume: 155
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19921550112

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✦ Synopsis

Abstract

We show for the three‐dimensional initial‐boundary value problem of the NAVIER‐STOKES and KELVIN‐VOIGT equation over bounded domains and for the corresponding stationary problem the existence of weak solutions in intermediate spaces between some of the usual spaces for weak solutions of the NAVIER‐STOKES equations and spaces for the corresponding strong solutions. The proofs yield estimates of the solutions in terms of the data which are supposed to be in appropriate intermediate spaces. The basic ingredients of the proof are well‐known results for weak and strong solutions and some nonlinear interpolation arguments.

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