Exponential attractors for 2d magneto-micropolor fluid flow in bounded domain
Kei Matsuura
We show the existence of an exponential attractor for the dynamical system associated with the equations of the system of the 2D magneto-micropolar fluid flow in a bounded domain. The construction of an exponential attractor relies on the abstract theory given in [2].
keywords: exponential attractor magneto-micropolar fluid.
Exponential attractors for a quasilinear parabolic equation
Kei Matsuura Mitsuharu Otani
Global attractors and exponential attractors are constructed for some quasilinear parabolic equations. The construction for the exponential attractor is carried out within the framework of the method of $l$-trajectories.
keywords: quasilinear parabolic equation. Exponential attractor
Well-posedness and large-time behaviors of solutions for a parabolic equation involving $p(x)$-Laplacian
Goro Akagi Kei Matsuura
This paper is concerned with the initial-boundary value problem for a nonlinear parabolic equation involving the so-called $p(x)$-Laplacian. A subdifferential approach is employed to obtain a well-posedness result as well as to investigate large-time behaviors of solutions.
keywords: $p(x)$-Laplacian subdifferential parabolic equation variable exponent Lebesgue and Sobolev spaces
Strong solutions of magneto-micropolar fluid equation
Hiroshi Inoue Kei Matsuura Mitsuharu Ôtani
We show the existence and uniqueness of a strong solution for the system of magneto-micropolar fluid motions under some assumptions on the regularity of given data similar to those of Fujita-Kato [4]. The method of our proof relies on the abstract nonmonotone perturbation theory developed in ˆ Otani [10].
keywords: nonmonotone perturbation theory. Magneto-micropolar fluids

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