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Dynamics of a fractional hydrodynamical equation for the Heisenberg paramagnet

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  • Pu, Xueke

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.

Suggested Citation

  • Pu, Xueke, 2015. "Dynamics of a fractional hydrodynamical equation for the Heisenberg paramagnet," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 213-229.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:213-229
    DOI: 10.1016/j.amc.2014.07.099
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    Cited by:

    1. Iskakova, Kulpash & Alam, Mohammad Mahtab & Ahmad, Shabir & Saifullah, Sayed & Akgül, Ali & Yılmaz, Gülnur, 2023. "Dynamical study of a novel 4D hyperchaotic system: An integer and fractional order analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 219-245.
    2. Xuan, Liu & Ahmad, Shabir & Ullah, Aman & Saifullah, Sayed & Akgül, Ali & Qu, Haidong, 2022. "Bifurcations, stability analysis and complex dynamics of Caputo fractal-fractional cancer model," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. Nyamoradi, Nemat & Rodríguez-López, Rosana, 2015. "On boundary value problems for impulsive fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 874-892.

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