Bornes sur la densité pour les équations de Navier-Stokes compressibles isentropiques avec conditions aux limites de Dirichlet
✍ Scribed by Pierre-Louis Lions
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 249 KB
- Volume
- 328
- Category
- Article
- ISSN
- 0764-4442
No coin nor oath required. For personal study only.
✦ Synopsis
Nous montrons que les bornes locales sur la densite, &ablies dans Lm travail prCcCdent de I'auteur, pour les solutions des equations de Navier-Stokes compressibles isentropiques avec des conditions aux lilnites de Dirichlet sont en fait valables jusqu'au
'IL E L2(0,T; H;(R))'Vno ice that this requirement incorporates homogeneous Dirichlet boundary t' conditions on ZL--, and the above equations hold in distributions sense.
We impose initial conditions on p and NIL, namely ~1,~~ = pO, p,ultCo = 7~ in fl and we assume that po 2 0, po E L^1(12), rno E L"?/(r+')(ft)", TUJJ = 0 as. on {pO = 0) and y (defined to be 0 on {PO = 0)) E Ll(fi).
Our main result the following:
THEOREM 1. -If y 2 i when IV = 2, y 2 i when L%~ = 3, y > T when N 2 4, there exists a solution (p,,u) such that p E L"(s1 x (0, T)) with p = (1 + ;)y -1.
The main new fact in the preceding result, compared to Theorem 7.2 in P.-L. Lions [3], is the fact that the bound in L" is shown to hold up to the boundary.