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On N AVIER ‐S TOKES and K ELVIN ‐V OIGT Equations in Three Dimensions in Interpolation Spaces
Author(s) -
Böhm Michael
Publication year - 1992
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19921550112
Subject(s) - mathematics , interpolation (computer graphics) , bounded function , mathematical proof , nonlinear system , boundary (topology) , pure mathematics , mathematical analysis , computer science , geometry , physics , telecommunications , frame (networking) , quantum mechanics
We show for the three‐dimensional initial‐boundary value problem of the N AVIER ‐S TOKES and K ELVIN ‐V OIGT 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 N AVIER ‐S TOKES 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.