TY - JOUR
T1 - Generalized Forchheimer Flows of Isentropic Gases
AU - Celik, Emine
AU - Hoang, Luan
AU - Kieu, Thinh
N1 - Funding Information:
L. H. acknowledges the support by NSF Grant DMS-1412796.
Publisher Copyright:
© 2016, Springer International Publishing.
PY - 2018/3/1
Y1 - 2018/3/1
N2 - We consider generalized Forchheimer flows of either isentropic gases or slightly compressible fluids in porous media. By using Muskat’s and Ward’s general form of the Forchheimer equations, we describe the fluid dynamics by a doubly nonlinear parabolic equation for the appropriately defined pseudo-pressure. The volumetric flux boundary condition is converted to a time-dependent Robin-type boundary condition for this pseudo-pressure. We study the corresponding initial boundary value problem, and estimate the L∞ and W1 , 2 - a (with 0 < a< 1) norms for the solution on the entire domain in terms of the initial and boundary data. It is carried out by using a suitable trace theorem and an appropriate modification of Moser’s iteration.
AB - We consider generalized Forchheimer flows of either isentropic gases or slightly compressible fluids in porous media. By using Muskat’s and Ward’s general form of the Forchheimer equations, we describe the fluid dynamics by a doubly nonlinear parabolic equation for the appropriately defined pseudo-pressure. The volumetric flux boundary condition is converted to a time-dependent Robin-type boundary condition for this pseudo-pressure. We study the corresponding initial boundary value problem, and estimate the L∞ and W1 , 2 - a (with 0 < a< 1) norms for the solution on the entire domain in terms of the initial and boundary data. It is carried out by using a suitable trace theorem and an appropriate modification of Moser’s iteration.
UR - http://www.scopus.com/inward/record.url?scp=85042521355&partnerID=8YFLogxK
U2 - 10.1007/s00021-016-0313-2
DO - 10.1007/s00021-016-0313-2
M3 - Article
AN - SCOPUS:85042521355
VL - 20
SP - 83
EP - 115
JO - Journal of Mathematical Fluid Mechanics
JF - Journal of Mathematical Fluid Mechanics
SN - 1422-6928
IS - 1
ER -