An existence theorem for the Boussinesq equations with non-Dirichlet boundary conditions

Zdeněk Skalák; Petr Kučera

Applications of Mathematics (2000)

  • Volume: 45, Issue: 2, page 81-98
  • ISSN: 0862-7940

Abstract

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The evolution Boussinesq equations describe the evolution of the temperature and velocity fields of viscous incompressible Newtonian fluids. Very often, they are a reasonable model to render relevant phenomena of flows in which the thermal effects play an essential role. In the paper we prescribe non-Dirichlet boundary conditions on a part of the boundary and prove the existence and uniqueness of solutions to the Boussinesq equations on a (short) time interval. The length of the time interval depends only on certain norms of the given data. In the proof we use a fixed point theorem method in Sobolev spaces with non-integer order derivatives. The proof is performed for Lipschitz domains and a wide class of data.

How to cite

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Skalák, Zdeněk, and Kučera, Petr. "An existence theorem for the Boussinesq equations with non-Dirichlet boundary conditions." Applications of Mathematics 45.2 (2000): 81-98. <http://eudml.org/doc/33050>.

@article{Skalák2000,
abstract = {The evolution Boussinesq equations describe the evolution of the temperature and velocity fields of viscous incompressible Newtonian fluids. Very often, they are a reasonable model to render relevant phenomena of flows in which the thermal effects play an essential role. In the paper we prescribe non-Dirichlet boundary conditions on a part of the boundary and prove the existence and uniqueness of solutions to the Boussinesq equations on a (short) time interval. The length of the time interval depends only on certain norms of the given data. In the proof we use a fixed point theorem method in Sobolev spaces with non-integer order derivatives. The proof is performed for Lipschitz domains and a wide class of data.},
author = {Skalák, Zdeněk, Kučera, Petr},
journal = {Applications of Mathematics},
keywords = {Boussinesq equations; non-Dirichlet boundary conditions; Sobolev space with non-integer order derivatives; Schauder principle; Boussinesq equations; non-Dirichlet boundary conditions; Sobolev space with non-integer order derivatives; Schauder principle},
language = {eng},
number = {2},
pages = {81-98},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An existence theorem for the Boussinesq equations with non-Dirichlet boundary conditions},
url = {http://eudml.org/doc/33050},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Skalák, Zdeněk
AU - Kučera, Petr
TI - An existence theorem for the Boussinesq equations with non-Dirichlet boundary conditions
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 2
SP - 81
EP - 98
AB - The evolution Boussinesq equations describe the evolution of the temperature and velocity fields of viscous incompressible Newtonian fluids. Very often, they are a reasonable model to render relevant phenomena of flows in which the thermal effects play an essential role. In the paper we prescribe non-Dirichlet boundary conditions on a part of the boundary and prove the existence and uniqueness of solutions to the Boussinesq equations on a (short) time interval. The length of the time interval depends only on certain norms of the given data. In the proof we use a fixed point theorem method in Sobolev spaces with non-integer order derivatives. The proof is performed for Lipschitz domains and a wide class of data.
LA - eng
KW - Boussinesq equations; non-Dirichlet boundary conditions; Sobolev space with non-integer order derivatives; Schauder principle; Boussinesq equations; non-Dirichlet boundary conditions; Sobolev space with non-integer order derivatives; Schauder principle
UR - http://eudml.org/doc/33050
ER -

References

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