Joanna Rencławowicz, Wojciech M. Zajączkowski (2006)
Applicationes Mathematicae
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We prove the existence of weak solutions to the Navier-Stokes equations describing the motion of a fluid in a Y-shaped domain.
Francis Ribaud (2002)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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K. K. Golovkin, A. Krzywicki (1967)
Colloquium Mathematicae
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Radim Hošek, Václav Mácha (2019)
Czechoslovak Mathematical Journal
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The coupled Navier-Stokes/Allen-Cahn system is a simple model to describe phase separation in two-component systems interacting with an incompressible fluid flow. We demonstrate the weak-strong uniqueness result for this system in a bounded domain in three spatial dimensions which implies that when a strong solution exists, then a weak solution emanating from the same data coincides with the strong solution on its whole life span. The proof of given assertion relies on a form of a relative...
R. Farwig, H. Kozono, H. Sohr (2011)
Rendiconti del Seminario Matematico della Università di Padova
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Elva Ortega-Torres, Marko Rojas-Medar (2009)
Rendiconti del Seminario Matematico della Università di Padova
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Skalák, Zdeněk, Kučera, Petr (2001)
Commentationes Mathematicae Universitatis Carolinae
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Zdeněk Skalák, Petr Kučera (2001)
Commentationes Mathematicae Universitatis Carolinae
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Some results on regularity of weak solutions to the Navier-Stokes equations published recently in [3] follow easily from a classical theorem on compact operators. Further, weak solutions of the Navier-Stokes equations in the space are regular.
Patrick Penel, Milan Pokorný (2004)
Applications of Mathematics
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We study the nonstationary Navier-Stokes equations in the entire three-dimensional space and give some criteria on certain components of gradient of the velocity which ensure its global-in-time smoothness.