On non-homogeneous viscous incompressible fluids. Existence of regular solutions
Lemoine, Jérôme
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997), p. 697-715 / Harvested from Czech Digital Mathematics Library

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).

Publié le : 1997-01-01
Classification:  35B65,  35Q30,  76D05
@article{118967,
     author = {J\'er\^ome Lemoine},
     title = {On non-homogeneous viscous incompressible fluids.  Existence of regular solutions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {38},
     year = {1997},
     pages = {697-715},
     zbl = {0940.35153},
     mrnumber = {1603698},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118967}
}
Lemoine, Jérôme. On non-homogeneous viscous incompressible fluids.  Existence of regular solutions. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 697-715. http://gdmltest.u-ga.fr/item/118967/

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.

Dunford N.; Schwartz J.T. Linear Operators, Interscience, 1958. | Zbl 0635.47003

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.

Kabbaj M. Thesis, Blaise Pascal University, France, 1994.

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)

Lemoine J. Thesis, Blaise Pascal University, France, 1995.

Lions J.L. On Some Problems Connected with Navier-Stokes Equations in Nonlinear Evolution Equations, M.C. Crandall, ed., Academic Press, New York, 1978. | MR 0513812

Lions P.L. Mathematical Topics in Fluids Mechanics, Vol. I, Incompressible Models, Clarendon Press, Oxford, 1996. | MR 1422251

Simon J. Compact sets in the space $L^p(0,T;B)$, Ann. Mat. Pura Appl. IV, Vol. CXLVI, (1987), 65-96. | MR 0916688

Simon J. Nonhomogeneous viscous incompressible fluids: existence of velocity, density, and pressure, SIAM J. Math. Anal. 21 5 (1990), 1093-1117. (1990) | MR 1062395 | Zbl 0702.76039

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) | Zbl 0451.35092

Temam R. Navier-Stokes Equations, North-Holland (second edition), 1979. | Zbl 1157.35333

Triebel H. Interpolation Theory, Function Spaces, Differential Operators, North-Holland Publishing Company, 1978. | MR 0503903 | Zbl 0830.46028