Well-posedness for the motion of an incompressible liquid with free surface boundary
Annals of mathematics, Tome 162 (2005) no. 1, pp. 109-194
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We study the motion of an incompressible perfect liquid body in vacuum. This can be thought of as a model for the motion of the ocean or a star. The free surface moves with the velocity of the liquid and the pressure vanishes on the free surface. This leads to a free boundary problem for Euler’s equations, where the regularity of the boundary enters to highest order. We prove local existence in Sobolev spaces assuming a “physical condition”, related to the fact that the pressure of a fluid has to be positive.
@article{10_4007_annals_2005_162_109,
author = {Hans Lindblad},
title = {Well-posedness for the motion of an incompressible liquid with free surface boundary},
journal = {Annals of mathematics},
pages = {109--194},
publisher = {mathdoc},
volume = {162},
number = {1},
year = {2005},
doi = {10.4007/annals.2005.162.109},
mrnumber = {2178961},
zbl = {1095.35021},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.162.109/}
}
TY - JOUR AU - Hans Lindblad TI - Well-posedness for the motion of an incompressible liquid with free surface boundary JO - Annals of mathematics PY - 2005 SP - 109 EP - 194 VL - 162 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.162.109/ DO - 10.4007/annals.2005.162.109 LA - en ID - 10_4007_annals_2005_162_109 ER -
%0 Journal Article %A Hans Lindblad %T Well-posedness for the motion of an incompressible liquid with free surface boundary %J Annals of mathematics %D 2005 %P 109-194 %V 162 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.162.109/ %R 10.4007/annals.2005.162.109 %G en %F 10_4007_annals_2005_162_109
Hans Lindblad. Well-posedness for the motion of an incompressible liquid with free surface boundary. Annals of mathematics, Tome 162 (2005) no. 1, pp. 109-194. doi: 10.4007/annals.2005.162.109
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