On non-homogeneous viscous incompressible fluids. Existence of regular solutions

Jérôme Lemoine

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 4, page 697-715
  • ISSN: 0010-2628

Abstract

top
We consider the flow of a non-homogeneous viscous incompressible fluid which is known at an initial time. Our purpose is to prove that, when Ω is smooth enough, there exists a local strong regular solution (which is global for small regular data).

How to cite

top

Lemoine, Jérôme. "On non-homogeneous viscous incompressible fluids. Existence of regular solutions." Commentationes Mathematicae Universitatis Carolinae 38.4 (1997): 697-715. <http://eudml.org/doc/248065>.

@article{Lemoine1997,
abstract = {We consider the flow of a non-homogeneous viscous incompressible fluid which is known at an initial time. Our purpose is to prove that, when $\Omega $ is smooth enough, there exists a local strong regular solution (which is global for small regular data).},
author = {Lemoine, Jérôme},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Navier-Stokes equations; non-homogeneous viscous incompressible fluids; existence; local regular solution; regular data; the positiveness of the density},
language = {eng},
number = {4},
pages = {697-715},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On non-homogeneous viscous incompressible fluids. Existence of regular solutions},
url = {http://eudml.org/doc/248065},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Lemoine, Jérôme
TI - On non-homogeneous viscous incompressible fluids. Existence of regular solutions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 4
SP - 697
EP - 715
AB - We consider the flow of a non-homogeneous viscous incompressible fluid which is known at an initial time. Our purpose is to prove that, when $\Omega $ is smooth enough, there exists a local strong regular solution (which is global for small regular data).
LA - eng
KW - Navier-Stokes equations; non-homogeneous viscous incompressible fluids; existence; local regular solution; regular data; the positiveness of the density
UR - http://eudml.org/doc/248065
ER -

References

top
  1. Antonzev S.A., Kajikov A.V., Mathematical study of flows of nonhomogeneous fluids (in Russian), Lectures at the University of Novosibirsk, Novosibirsk, U.S.S.R., 1973. 
  2. Dunford N., Schwartz J.T., Linear Operators, Interscience, 1958. Zbl0635.47003
  3. Fernández-Cara E., Guillén F., Some new results for the variable density Navier-Stokes equations, Ann. Fac. Sci. Toulouse Math., Vol II, no. 2, 1993. 
  4. Kabbaj M., Thesis, Blaise Pascal University, France, 1994. 
  5. Ladyzenskaya O.A., Solonnikov V.A., Unique solvability of an initial-and boundary-value problem for viscous incompressible nonhomogeneous fluids, J. Soviet. Math. 9 (1978), 697-749. (1978) 
  6. Lemoine J., Thesis, Blaise Pascal University, France, 1995. 
  7. Lions J.L., On Some Problems Connected with Navier-Stokes Equations in Nonlinear Evolution Equations, M.C. Crandall, ed., Academic Press, New York, 1978. MR0513812
  8. Lions P.L., Mathematical Topics in Fluids Mechanics, Vol. I, Incompressible Models, Clarendon Press, Oxford, 1996. MR1422251
  9. Simon J., Compact sets in the space L p ( 0 , T ; B ) , Ann. Mat. Pura Appl. IV, Vol. CXLVI, (1987), 65-96. MR0916688
  10. Simon J., Nonhomogeneous viscous incompressible fluids: existence of velocity, density, and pressure, SIAM J. Math. Anal. 21 5 (1990), 1093-1117. (1990) Zbl0702.76039MR1062395
  11. Solonnikov V.A., Solvability of the initial-boundary-value problem for the equations of motion of a viscous compressible fluid, J. Soviet. Math. 14 2 (1980), 1120-1133. (1980) Zbl0451.35092
  12. Temam R., Navier-Stokes Equations, North-Holland (second edition), 1979. Zbl1157.35333
  13. Triebel H., Interpolation Theory, Function Spaces, Differential Operators, North-Holland Publishing Company, 1978. Zbl0830.46028MR0503903

NotesEmbed ?

top

You must be logged in to post comments.