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Well-posedness of two-phase Darcy flow in 3D
Author(s):
David
M.
Ambrose
Journal:
Quart. Appl. Math.
65
(2007),
189-203.
MSC (2000):
Primary 35Q35
Posted:
February 12, 2007
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Abstract:
We prove the well-posedness, locally in time, of the motion of two fluids flowing according to Darcy's law, separated by a sharp interface in the absence of surface tension. We first reformulate the problem using favorable variables and coordinates. This results in a quasilinear parabolic system. Energy estimates are performed, and these estimates imply that the motion is well-posed for a short time with data in a Sobolev space, as long as a condition is satisfied. This condition essentially says that the more viscous fluid must displace the less viscous fluid. It should be true that small solutions exist for all time; however, this question is not addressed in the present work.
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Additional Information:
David
M.
Ambrose
Affiliation:
Department of Mathematical Sciences, Clemson University, Martin Hall, Clemson, South Carolina 29634
PII:
S0033-569X-07-01055-3
Received by editor(s):
November 16, 2006
Posted:
February 12, 2007
Additional Notes:
The author was supported by NSF grant DMS-0610898
Copyright of article:
Copyright
2007,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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