Open Access$L^p$-theory for the Navier-Stokes equations with pressure boundary conditions
Author(s) -
Chérif Amrouche,
Nour El Houda Seloula
Publication year - 2013
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2013.6.1113
Subject(s) - mathematics , bounded function , class (philosophy) , navier–stokes equations , boundary (topology) , mathematical analysis , boundary value problem , fixed point theorem , type (biology) , open set , pure mathematics , physics , compressibility , computer science , mechanics , ecology , artificial intelligence , biology
International audienceWe consider the Navier-Stokes equations with pressure boundary conditions in the case of a bounded open set, connected of class C 1;1 of ℝ3. We prove existence of solution by using a fixed point theorem over the type-Oseen problem. This result was studied in [5] in the Hilbertian case. In our study we give the Lp-theory for 1 < p < ∞