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On the global regularity of generalized Leray-alpha type models. (English) Zbl 1233.35064
Summary: We generalize Leray-alpha type models studied in [A. Cheskidov et al., Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 461, No. 2055, 629–649 (2005; Zbl 1145.76386); J. S. Linshiz and E. S. Titi, J. Math. Phys. 48, No. 6, 065504, 28 p. (2007; Zbl 1144.81378)] via fractional Laplacians and employ Besov space techniques to obtain global regularity results with the logarithmically supercritical dissipation.

35B65 Smoothness and regularity of solutions to PDEs
35Q35 PDEs in connection with fluid mechanics
35Q86 PDEs in connection with geophysics
35R11 Fractional partial differential equations
Full Text: DOI
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