No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

Let$X$(-ϱ$B$^{$m$}×$C$^{$n$}be a compact set over the unit sphere ϱ$B$^{$m$}such that for each$z$∈ϱ$B$^{$m$}the fiber$X$_{$z$}={ω∈$C$^{$n$};($z, ω$)∈$X$} is the closure of a completely circled pseudoconvex domain in$C$^{$n$}. The polynomial hull $$\hat X$$ of$X$is described in terms of the Perron-Bremermann function for the homogeneous defining function of$X$. Moreover, for each point ($z$_{0},$w$_{0})∈Int $$\hat X$$ there exists a smooth up to the boundary analytic disc$F$:Δ→$B$^{$m$}×$C$^{$n$}with the boundary in$X$such that$F$(0)=($z$_{0},$w$_{0}).

ABSTRACT We investigate a kinetic model for the sedimentation of dilute suspensions of rod-like particles under gravity, deduced by Helzel, Otto, and Tzavaras (2011), which couples the impressible (Navier-)Stokes equation with the Fokker-Planck equation. With a no-flux boundary condition for the distribution function, we establish the existence and uniqueness of a global weak solution to the two dimensional model involving the Stokes equation.