We consider a coupled Patlak-Keller-Segel-Navier-Stokes system in $\mathbb{R}^2$ that describes the collective motion of cells and fluid flow, where are attracted by chemical substance transported ambient velocity, flow is forced friction induced cells. The main result paper to show global existence free-energy solutions 2D with critical subcritical mass.

Fractional factorial split-plot designs are widely used when it is impractical to perform fractional experiments in a completely random order. When there too many subplots per whole plot, or few plots, with replicated settings of the plot factors preferred. However, such an important study undeveloped literature. This paper considers WP from viewpoint clear effects. We investigate sufficient an...

In some experiments, the levels of factors are difficult to change; then fractional factorial split-plot (FFSP) designs suitable for selection. an FFSP design, divided into two classes—the whole plot (WP) and subplot (SP) factors. selection WP can affect that SP factors, which attracts much attention Paying more a new optimality criterion selecting such is proposed. The robustness proposed meth...

Abstract. The meta-plot is a descriptive visual tool for meta-analysis that provides information on the primary studies in and results of meta-analysis. More precisely, portrays (1) precision statistical power meta-analysis, (2) estimate confidence interval random-effects (3) cumulative yielding robustness check meta-analytic effect size with respect to studies’ precision, (4) evidence publicat...

The L-critical parabolic-elliptic Patlak-Keller-Segel system is a classical model of chemotactic aggregation in micro-organisms well-known to have critical mass phenomena [10, 8]. In this paper we study this critical mass phenomenon in the context of Patlak-Keller-Segel models with spatially varying diffusivity and decay rate of the chemo-attractant. The primary tool for the proof of global exi...