Marco Cannone, Fabrice Planchon (2000)
Revista Matemática Iberoamericana
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We derive various estimates for strong solutions to the Navier-Stokes equations in C([0,T),L(R)) that allow us to prove some regularity results on the kinematic bilinear term.
Marco Cannone (1997)
Revista Matemática Iberoamericana
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We generalize a classical result of T. Kato on the existence of global solutions to the Navier-Stokes system in C([0,∞);L(R)). More precisely, we show that if the initial data are sufficiently oscillating, in a suitable Besov space, then Kato's solution exists globally. As a corollary to this result, we obtain a theory of existence of self-similar solutions for the Navier-Stokes equations.
F. Planchon (1996)
Annales de l'I.H.P. Analyse non linéaire
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R. Farwig, H. Kozono, H. Sohr (2011)
Rendiconti del Seminario Matematico della Università di Padova
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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.
P.-L. Lions, N. Masmoudi (1999)
Annales de l'I.H.P. Analyse non linéaire
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