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Existence and Regularity of a Class of Weak Solutions to the Navier–Stokes Equations

✍ Scribed by Cheng He

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
241 KB
Volume
210
Category
Article
ISSN
0022-247X

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✦ Synopsis

We construct a class of weak solutions to the Navier᎐Stokes equations, which have second order spatial derivatives and one order time derivatives, of p power s Ž 2, r Ž .. summability for 1p F 5r4. Meanwhile, we show that u g L 0, T ; W ⍀ with 1rs q 3r2 r s 2 for 1r F 5r4. r can be relaxed not to exceed 3r2 if we consider only in the interior of ⍀. In the end, we extend the classical regularity s Ž r Ž .. theorem. Our results show that u is a regular solution if ٌu g L 0, T ; L ⍀ with Ž . 1rsq3r2rs1 for ⍀ satisfying 1.3 , with 1rs q 1rr s 5r6 for arbitrary domain in R 3 and 1s F 2. For ⍀ s R n with n G 3, this result was previously Ž .

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