We study the Stokes operator A in a threedimensional Lipschitz domain Ω. Our main result asserts that the domain of A is contained in W 1,p 0 (Ω)∩W (Ω) for some p > 3. Certain L∞-estimates are also established. Our results may be used to improve the regularity of strong solutions of Navier-Stokes equations in nonsmooth domains. In the appendix we provide a simple proof of area integral estimate...

Uniform three-dimensional ellipsoidal distributions of charge are the ultimate goal in charged particle accelerator physics because of their linear internal force fields. Such bunches remain ellipsoidal with perfectly linear position-momentum phase space correlations in any linear transport system. We present a method, based on photoemission by radially shaped femtosecond laser pulses, to actua...

The boundary value problem for the steady Navier–Stokes system is considered in a 2D multiply-connected bounded domain with having power cusp singularity at point O. case of nonzero flow rates over connected components studied. It also supposed that there source/sink In this solution necessarily has an infinite Dirichlet integral. existence to proved assuming are “sufficiently small”. This cond...

We propose a generalized treatment of the drag force of a spherical particle due to its motion in a laminar fluid media. The theory is equally applicable to analysis of particle diffusion and electric mobility. The focus of the current analysis is on the motion of spherical particles in low-density gases with Knudsen number Kn>>1. The treatment is based on the gas-kinetic theory analysis of dra...

A general framework for the description of classic wave propagation is introduced. This relies on a cone structure C determined by an intrinsic space ? velocities (point, direction and time-dependent) observers’ vector field ???t whose integral curves provide both Zermelo problem auxiliary Lorentz–Finsler metric G compatible with C. The PDE wavefront reduced to ODE t-parametrized geodesics Part...

Control problems with hard bounds on the control values, restrictions on the state trajectory over a finite time horizon, and guaranteed behavior despite the disturbances, are difficult to solve using frequency based design methods. Such problems have received much attention over the past decade. In order to address them one needs to study system evolution in the time domain. The central concep...

Jaydeep P. Bardhan and Matthew G. Knepley Dept. of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago IL 60612 Computation Institute, The University of Chicago, Chicago IL 60637 Abstract We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are us...