Dynamics of a fractional hydrodynamical equation for the Heisenberg paramagnet

Xueke Pu

Applied Mathematics and Computation, 2015, vol. 257, issue C, 213-229

Abstract: In the present work, we study the global solvability and large time dynamics for a fractional generalization of the hydrodynamical equation modeling the soft micromagnetic materials. Introducing a cancellation property, we prove the existence of weak solutions and establish a uniqueness criterion. A maximal principle is obtained and the global existence and uniqueness of smooth solutions are proved by some a priori estimates. Finally, we analyze the asymptotic behavior of the solutions within the theory of infinite dimensional dissipative dynamical systems. We prove that the problem generates a strongly continuous semigroup on a suitable phase space and show the existence of a maximal global attractor A in this phase space. Moreover, in absence of external force, global attractor A converges exponentially to a single equilibrium.

Keywords: Fractional hydrodynamical equation; Weak solutions; Decay estimate; Smooth solutions; Global attractors (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:257:y:2015:i:c:p:213-229

DOI: 10.1016/j.amc.2014.07.099

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