A criterion is given for the convergence of numerical solutions of the Navier-Stokes equations in two dimensions under steady conditions. The criterion applies to all cases, of steady viscous flow in two dimensions and shows that if the local ' mesh Reynolds number ', based on the size of the mesh used in the solution, exceeds a certain fixed value, the numerical solution will not converge.

On the Navier-Stokes equations

It is shown that the L3,∞-solutions of the Cauchy problem for the three-dimensional Navier-Stokes equations are smooth.

http://www.pdmi.ras.ru/~seregin/Recent%20Publications/engESS3.pdf

L3,∞-solutions of the Navier-Stokes equations and backward uniqueness

We prove regularity results for weak solutions to systems modelling electro-rheological fluids in the stationary case, as proposed in [27, 31]; a particular case of the system we consider is

/pdf/regularity-results-for-stationary-electro-rheological-fluids-4paa2azehn.pdf

Regularity Results for Stationary Electro-Rheological Fluids

nonlinear functional analysis and its applications is available in our book collection an online access to it is set as public so you can get it instantly. Our books collection hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the nonlinear functional analysis and its applications is universally compatible with any devices to read.

Nonlinear Functional Analysis And Its Applications

We prove the boundedness of the Hardy–Littlewood maximal function on the generalized Lebesgue space Lp(·)(Rd) under a continuity assumption on p that is weaker than uniform Holder continuity. We deduce continuity of mollifying sequences and density of C∞(Ω) in W1,p(·)(Ω) . Mathematics subject classification (2000): 42B25, 46E30.

/pdf/maximal-function-on-generalized-lebesgue-spaces-l-p-cdot-3w7mbbs5lg.pdf

Maximal function on generalized Lebesgue spaces $L^{p(\cdot)}$

Modeling of electrorheological fluids.- Mathematical framework.- Electrorheological fluids with shear dependent viscosities: Steady flows.- Electrorheological fluids with shear dependent viscosities: Unsteady flows.

Electrorheological Fluids: Modeling and Mathematical Theory

This book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering

Weak and Measure-Valued Solutions to Evolutionary PDEs

/pdf/on-leray-s-self-similar-solutions-of-the-navier-stokes-ayq3k3poz4.pdf

On Leray's self-similar solutions of the Navier-Stokes equations

Calderón-Zygmund operators on generalized Lebesgue spaces $L^{p(\cdot)}$ and problems related to fluid dynamics

We prove the existence of weak solutions u : QT → Rn of the equations of unsteady motion of an incompressible fluid with shear-dependent viscosity in a cylinder QT = × (0, T ), where ⊂ Rn denotes a bounded domain. Under the assumption that the extra stress tensor S possesses a q-structure with q > 2n n+2 , we are able to construct a weak solution u ∈ Lq (0, T ; W 1,q 0 ( )) ∩ Cw([0, T ]; L2( )) with div u = 0. Our approach is based on the Lipschitz truncation method, which is new in this context. Mathematics Subject Classification (2000): 76D03(primary);35D05,46,34A34 (secondary).

/pdf/existence-of-weak-solutions-for-unsteady-motions-of-o8c54qr5r0.pdf

Michael Růžička

Papers

Electrorheological Fluids: Modeling and Mathematical Theory

Weak and Measure-Valued Solutions to Evolutionary PDEs

On Leray's self-similar solutions of the Navier-Stokes equations

Calderón-Zygmund operators on generalized Lebesgue spaces $L^{p(\cdot)}$ and problems related to fluid dynamics

Existence of weak solutions for unsteady motions of generalized Newtonian fluids