Statistical study of Navier-Stokes equations, I
C. Foiaş (1972)
Rendiconti del Seminario Matematico della Università di Padova
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C. Foiaş (1972)
Rendiconti del Seminario Matematico della Università di Padova
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Ciprian Foias, Ricardo M. S. Rosa, Roger Temam (2013)
Annales de l’institut Fourier
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This work is devoted to the concept of statistical solution of the Navier-Stokes equations, proposed as a rigorous mathematical object to address the fundamental concept of ensemble average used in the study of the conventional theory of fully developed turbulence. Two types of statistical solutions have been proposed in the 1970’s, one by Foias and Prodi and the other one by Vishik and Fursikov. In this article, a new, intermediate type of statistical solution is introduced and studied....
Dragos Iftimie (1999)
Revista Matemática Iberoamericana
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In this paper we prove global existence and uniqueness for solutions of the 3-dimensional Navier-Stokes equations with small initial data in spaces which are H in the i-th direction, δ + δ + δ = 1/2, -1/2 < δ < 1/2 and in a space which is L in the first two directions and B in the third direction, where H and B denote the usual homogeneous Sobolev and Besov spaces.
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.
Flandoli, Franco, Romito, Marco
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Jens Frehse, Michael Růžička (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Zubelevich, Oleg (2005)
Lobachevskii Journal of Mathematics
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