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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.

MSC:
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
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