Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid
Author
dc.contributor.author
San Martín, Jorge
Author
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Starovoitov, Victor
es_CL
Author
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Tucsnak, Marius
es_CL
Admission date
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2014-01-09T13:56:59Z
Available date
dc.date.available
2014-01-09T13:56:59Z
Publication date
dc.date.issued
2002
Cita de ítem
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Arch. Rational Mech. Anal. 161 (2002) 113–147
en_US
Identifier
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DOI: 10.1007/s002050100172
Identifier
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https://repositorio.uchile.cl/handle/2250/126101
General note
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Artículo de publicación ISI
en_US
Abstract
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We consider the two-dimensional motion of several non-homogeneous rigid
bodies immersed in an incompressible non-homogeneous viscous fluid. The fluid,
and the rigid bodies are contained in a fixed open bounded set of R2. The motion of
the fluid is governed by the Navier-Stokes equations for incompressible fluids and
the standard conservation laws of linear and angular momentum rule the dynamics
of the rigid bodies. The time variation of the fluid domain (due to the motion of the
rigid bodies) is not known a priori, so we deal with a free boundary value problem.
The main novelty here is the demonstration of the global existence of weak solutions
for this problem. More precisely, the global character of the solutions we obtain is
due to the fact that we do not need any assumption concerning the lack of collisions
between several rigid bodies or between a rigid body and the boundary. We give
estimates of the velocity of the bodies when their mutual distance or the distance
to the boundary tends to zero.