TY - JOUR
T1 - Global estimates for generalized Forchheimer flows of slightly compressible fluids
AU - Hoang, Luan
AU - Kieu, Thinh
N1 - Funding Information:
∗Supported by NSF grant DMS-1412796
Publisher Copyright:
© 2019, The Hebrew University of Jerusalem.
PY - 2019/3/1
Y1 - 2019/3/1
N2 - This paper is focused on the generalized Forchheimer flows of slightly compressible fluids in porous media. They are reformulated as a degenerate parabolic equation for the pressure. The initial boundary value problem is studied with time-dependent Dirichlet boundary data. The estimates up to the boundary and for all time are derived for the L∞-norm of the pressure, its gradient and time derivative. Large-time estimates are established to be independent of the initial data. Particularly, thanks to the special structure of the pressure’s nonlinear equation, the global gradient estimates are obtained in a relatively simple way, avoiding complicated calculations and a prior requirement of Hölder estimates.
AB - This paper is focused on the generalized Forchheimer flows of slightly compressible fluids in porous media. They are reformulated as a degenerate parabolic equation for the pressure. The initial boundary value problem is studied with time-dependent Dirichlet boundary data. The estimates up to the boundary and for all time are derived for the L∞-norm of the pressure, its gradient and time derivative. Large-time estimates are established to be independent of the initial data. Particularly, thanks to the special structure of the pressure’s nonlinear equation, the global gradient estimates are obtained in a relatively simple way, avoiding complicated calculations and a prior requirement of Hölder estimates.
UR - http://www.scopus.com/inward/record.url?scp=85058415540&partnerID=8YFLogxK
U2 - 10.1007/s11854-018-0064-5
DO - 10.1007/s11854-018-0064-5
M3 - Article
AN - SCOPUS:85058415540
VL - 137
SP - 1
EP - 55
JO - Journal d'Analyse Mathematique
JF - Journal d'Analyse Mathematique
SN - 0021-7670
IS - 1
ER -