Boundary Regularity of Weak Solutions of the Navier–Stokes Equations

Author: Choe, H.J.

Source: Journal of Differential Equations, Volume 149, Number 2, November 1998 , pp. 211-247(37)

Publisher: Academic Press

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Abstract:

We prove that a solution to Navier–Stokes equations is in L2(0, ∞: H2(Ω)) under the critical assumption that uLr, r, 3/r+2/r′1 with r3. A boundary L estimate for the solution is derived if the pressure on the boundary is bounded. Here our estimate is local. Indeed, employing Moser type iteration and the reverse Hölder inequality, we find an integral estimate for L-norm of u. Moreover the solution is C1, α continuous up to boundary if the tangential derivatives of the pressure on the boundary are bounded. Then, from the bootstrap argument a local higher regularity theorem follows, that is, the velocity is as regular as the boundary data of the pressure. Copyright 1998 Academic Press.

Document Type: Research Article

Affiliations: Department of Mathematics, KAIST, Taejon, 305-701, Republic of Korea

Publication date: November 1, 1998

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