Geodesic
On non-homogeneous viscous incompressible fluids. Existence of regular solutions
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 4, pp. 697-715.

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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).
Classification : 35B65, 35Q30, 76D05
Keywords: Navier-Stokes equations 
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     author = {Lemoine, J\'er\^ome},
     title = {On non-homogeneous viscous incompressible fluids.  {Existence} of regular solutions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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     zbl = {0940.35153},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_1997__38_4_a7/}
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Lemoine, Jérôme. On non-homogeneous viscous incompressible fluids.  Existence of regular solutions. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 4, pp. 697-715. http://geodesic.mathdoc.fr/item/CMUC_1997__38_4_a7/