TY - JOUR
T1 - On the Muskat problem
T2 - Global in time results in 2D and 3D
AU - Constantin, Peter
AU - Córdoba, Diego
AU - Gancedo, Francisco
AU - Rodríguez-Piazza, Luis
AU - Strain, Robert M.
N1 - Funding Information:
Research of the first author supported in part by NSF grants DMS-1209394 and DMS-1265132; research of the second and third authors supported in part by MCINN grant MTM2011-26696 (Spain); research of the fourth author supported in part by MCINN grant MTM2012-05622 (Spain); research of the fifth author supported in part by NSF grants DMS-1500916, DMS-1200747, and an Alfred P. Sloan Foundation Research Fellowship.
Publisher Copyright:
© 2016 by Johns Hopkins University Press.
PY - 2016/12
Y1 - 2016/12
N2 - This paper considers the three-dimensional Muskat problem in the stable regime. We obtain a conservation law which provides an L2 maximum principle for the fluid interface. We also show global in time existence for strong and weak solutions with initial data controlled by explicit constants. Furthermore we refine the available estimates to obtain global existence and uniqueness for strong solutions with larger initial data than we previously had in 2D. Finally we provide global in time results in spaces with critical regularity, giving solutions with bounded slope and time integrable bounded curvature.
AB - This paper considers the three-dimensional Muskat problem in the stable regime. We obtain a conservation law which provides an L2 maximum principle for the fluid interface. We also show global in time existence for strong and weak solutions with initial data controlled by explicit constants. Furthermore we refine the available estimates to obtain global existence and uniqueness for strong solutions with larger initial data than we previously had in 2D. Finally we provide global in time results in spaces with critical regularity, giving solutions with bounded slope and time integrable bounded curvature.
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U2 - 10.1353/ajm.2016.0044
DO - 10.1353/ajm.2016.0044
M3 - Article
AN - SCOPUS:85006154598
SN - 0002-9327
VL - 138
SP - 1455
EP - 1494
JO - American Journal of Mathematics
JF - American Journal of Mathematics
IS - 6
ER -