On asymptotic behaviors of solutions to parabolic systems modelling chemotaxis

AbstractThis paper deals with large time behaviors of solutions to a Keller–Segel system which possesses self-similar solutions. By taking into account the invariant properties of the equation with respect to a scaling and translations, we show that suitably shifted self-similar solutions give more precise asymptotic profiles of general solutions at large time. The convergence rate is also computed in details

Asymptotic behavior of solution of the non-resistive 2D MHD equations on the half space

In this paper, we obtain the global well-posedness and the asymptotic behavior of solution of non-resistive 2D MHD problem on the half space. We overcome the difficulty of zero spectrum gap by building the relationship between half space and the whole space, and get the resolvent estimate for the weak diffusion system. We use the two-tier energy method that couples the boundedness of high-order $(H^3)$ energy to the decay of low-order energy, the latter of which is necessary to control the growth of the highest energy

On the Chorin method for thermal convection equations for viscous incompressible fluids (Regularity, singularity and long time behavior for partial differential equations with conservation law)

"Regularity, singularity and long time behavior for partial differential equations with conservation law". June 6-8, 2016. edited by Keiichi Kato, Mishio Kawashita, Masashi Misawa and Takayoshi Ogawa. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.Stability of stationary solutions of the Oberbeck Boussinesq system and the corresponding artificial compressible system is considered. The former system is obtained by a singular limit of zero artificial Mach number in the latter system. This paper overviews recent results on a relation of the stability of stationary solutions between both systems from the viewpoint of the singular perturbation