کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6420449 | 1631797 | 2015 | 17 صفحه PDF | دانلود رایگان |
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.
Journal: Applied Mathematics and Computation - Volume 257, 15 April 2015, Pages 213-229