Global existence and uniqueness of solution of the initial boundary value problem for a class of non-Newtonian fluids with vacuum

The aims of this paper are to discuss global existence and uniqueness of solution for a class of non-Newtonian fluids with vacuum in one-dimensional bounded interval. The important point in this paper is that we allow the initial vacuum. In particular, these results are used to prove similar results for more general non-Newtonian fluids, and applied to numerical computation. This work is partially supported by the 985 program of Jilin University, China Postdoctoral Sciences Foundation, and NSF Grant ([10571072]; [10601009]).     

Global regularity of solutions of 2D Boussinesq equations with fractional diffusion

The goal of this work is to study the Boussinesq equations for an incompressible fluid in R², with diffusion modeled by fractional Laplacian. The existence, the uniqueness and the regularity of solution has been proved.     

The lifespan of solutions to the inviscid 3D Boussinesq system

In this paper, we consider the inviscid 3D Boussinesq system in Besov spaces and obtain the lower bound for the lifespan of solutions.     

Global regularity for the 2D Oldroyd‐B model in the corotational case

This paper is dedicated to the Oldroyd‐B model with fractional dissipation (?Δ)^ατ for any α > 0. We establish the global smooth solutions to the Oldroyd‐B model in the corotational case with arbitrarily small fractional powers of the Laplacian in two spatial dimensions. Moreover, in the Appendix, we provide some a priori estimates to the Oldroyd‐B model in the critical case, which may be useful and of interest for future improvement. Therefore, our result is closer to the resolution of the well‐known global regularity issue on the critical 2D Oldroyd‐B model. Copyright © 2016 John Wiley & Sons, Ltd.     

Life span of solutions with large initial data for a class of coupled parabolic systems

This paper deals with a class of coupled systems of parabolic equations subject to large initial data. By constructing and solving a new ODE system, we obtain the accurate life span of solutions (blow-up time) of the expression determined by the initial value.     

Influence of Ti nanocrystallization on microstructure, interface bonding, surface energy and blood compatibility of surface TiO2 films

Recent progress in ultrafine-grained/nano-grained (UFG/NG) titanium permits a consideration for TiO₂ films deposited on nano-grained titanium for antithrombogenic application such as artificial valves and stents. For this paper, the microstructure, interface bonding, surface energy, and blood compatibility features of TiO₂ films deposited by direct current magnetron reactive sputtering technology on NG titanium and coarse-grained (CG) titanium were investigated. The results show that the nanocrystallization of titanium substrate has a significant influence on TiO₂ films. At the same deposition parameters, the content of rutile phase of TiO₂ film was increased from 47% (on the CG titanium substrate) to 72% (on the NG titanium substrate); the adhesion of TiO₂ film was improved from 5.8 N to 17 N; the surface energy was reduced from 6.37 dyn/cm to 3.01 dyn/cm; the clotting time was improved from 18 min to 28 min; the platelets accumulation and pseudopodium of adherent platelets on TiO₂ film on NG titanium were considerably reduced compared to that on CG titanium. The present results demonstrate the possibility of improving the blood compatibility of TiO₂ film through the approach of substrate nanocrystallization. Also it may provide an attractive idea to prepare stents with biological coatings of more outstanding blood compatibility and interface bonding.     

Yudovich type solution for the 2D inviscid Boussinesq system with critical and supercritical dissipation

In this paper we consider the Yudovich type solution of the 2D inviscid Boussinesq system with critical and supercritical dissipation. For the critical case, we show that the system admits a global and unique Yudovich type solution; for the supercritical case, we prove the local and unique existence of Yudovich type solution, and the global result under a smallness condition of _θ0${\theta }_0$. We also give a refined blowup criterion in the supercritical case.