We consider the initial-boundary value problem (IBVP) for the isentropic compressible Navier-Stokes equations (CNS) in the domain exterior to a ball in R d (d = 2 or 3). When viscosity coefficients are given as a constant multiple of the mass density ρ, based on some analysis of the nonlinear structure of this system, we prove the global existence of the unique spherically symmetric classical solution for (large) initial data with spherical symmetry and far field vacuum in some inhomogeneous Sobolev spaces. Moreover, the solutions we obtained have the conserved total mass and finite total energy. ρ keeps positive in the domain considered but decays to zero in the far field, which is consistent with the facts that the total mass is conserved, and CNS is a model of non-dilute fluids where ρ is bounded away from the vacuum. To prove the existence, on the one hand, we consider a well-designed reformulated structure by introducing some new variables, which, actually, can transfer the degeneracies of the time evolution and the viscosity to the possible singularity of some special source terms. On the other hand, it is observed that, for the spherically symmetric flow, the radial projection of the so-called effective velocity v = U + ∇ϕ(ρ) (U is the velocity of the fluid, and ϕ(ρ) is a function of ρ defined via the shear viscosity coefficient µ(ρ): ϕ ′ (ρ) = 2µ(ρ)/ρ 2 ), verifies a damped transport equation which provides the possibility to obtain its upper bound. Then combined with the BD entropy estimates, one can obtain the required uniform a priori estimates of the solution. It is worth pointing out that the frame work on the well-posedness theory established here can be applied to the shallow water equations.

Sevoflurane preconditioning has been proved to possess therapeutic effects on stress. However, the mechanism by which sevoflurane preconditioning protects against stress remains unclear. In this study, an acute model of heat stress in C.eleans was established. We investigated the dose-response of sevoflurane exposure on coordinated movement in C.elegans and time course for protection against heat stress of sevoflurane preconditioning to determine the optimal concentration and time point in the following experiments. EC99 of sevoflurane is 1.7% (1.3EC50) and sevoflurane preconditioning exerts the maximal protection at 6 hours after incubation, and these 2 parameters were used in our following experiments. We found that sevoflurane preconditioning increased DAF-16 nuclear translocation and enhanced the expression of DAF-16 during heat stress in N2 strain of C.elegans. DAF-16 mutation abolished the sevoflurane preconditioning-induced protection for heat stress. Furthermore, suppression of IMB-2 by RNAi prevented the upregulation of DAF-16 and enhancement of stress resistance caused by sevoflurane preconditioning. Overall, this work reveals that sevoflurane preconditioning increases the expression of DAF-16 via IMB-2 to enhance the stress resistance of C.elegans.

In this paper, we investigate the asymptotic behaviour of stochastic pantograph delay evolution equations driven by a tempered fractional Brownian motion (tfBm) with Hurst parameter H > 1/2. First of all, the global existence, uniqueness and mean square stability with general decay rate of mild solutions are established. In particular, we would like to point out that our analysis is not necessary to construct Lyapunov functions, but we deal directly with stability via the Banach fixed point theorem, the fractional power of operators and the semigroup theory. It is worth emphasizing that a novel estimate of stochastic integrals with respect to tfBm is presented, which greatly contributes to the stability analyses. Then after extending the factorization formula to the tfBm case, we construct the nontrivial equilibrium solution, defined for t ∈ R, by means of an approximation technique and a convergence analysis. Moreover, we analyze the Hölder regularity in time and general stability (including both polynomial and logarithmic stability) of the nontrivial equilibrium solution in the sense of mean square. As an example of application, the reaction diffusion neural network system with pantograph delay is considered, and the nontrivial equilibrium solution and general stability of the system are proved under the Lipschitz assumption.

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