Existence of solutions and Gevrey class regularity for Leray-alpha equations |
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Authors: | Yong-Jiang Yu Kai-Tai Li |
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Affiliation: | College of Sciences, Xi'an Jiaotong University, Xi'an 710049, China |
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Abstract: | In this paper we consider some equations similar to Navier-Stokes equations, the three-dimensional Leray-alpha equations with space periodic boundary conditions. We establish the regularity of the equations by using the classical Faedo-Galerkin method. Our argument shows that there exist an unique weak solution and an unique strong solution for all the time for the Leray-alpha equations, furthermore, the strong solutions are analytic in time with values in the Gevrey class of functions (for the space variable). The relations between the Leray-alpha equations and the Navier-Stokes equations are also considered. |
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Keywords: | Weak solution Strong solution Leray-alpha equations Navier-Stokes equations |
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