Generalized Forchheimer Flows of Isentropic Gases

Generalized Forchheimer Flows of Isentropic Gases 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 $$L^\infty $$ L ∞ and $$W^{1,2-a}$$ W 1 , 2 - a (with $$0<a<1$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Fluid Mechanics Springer Journals

Generalized Forchheimer Flows of Isentropic Gases

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Publisher
Springer International Publishing
Copyright
Copyright © 2016 by Springer International Publishing
Subject
Physics; Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics
ISSN
1422-6928
eISSN
1422-6952
D.O.I.
10.1007/s00021-016-0313-2
Publisher site
See Article on Publisher Site

Abstract

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 $$L^\infty $$ L ∞ and $$W^{1,2-a}$$ W 1 , 2 - a (with $$0<a<1$$ 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.

Journal

Journal of Mathematical Fluid MechanicsSpringer Journals

Published: Jan 2, 2017

References

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