global strong solutions of two dimensional navier stokes equations with nonlinear slip boundary conditions abstract the two dimensional time dependent navier stokes equations with nonlinear slip boundary conditions are investigated in this paper since the nonlinear slip boundary conditions of this type include the subdifferential property the weak variational formulation is the variational inequality the existence uniqueness and regularity of global weak solutions are shown using the regularized method moreover the continuous dependence property of the weak solution for given initial data and the behavior of the global weak solution as t are established

modules and matrices abstract noncommutative ring theory was described in terms of matrices in its earliest days we give some examples showing how matrix theory can now in turn profit from the theory of rings and modules

on the vanishing viscosity limit for the 3d navier stokes equations with a slip boundary condition where and below and denote the div and curl operators respectively n is the outward normal and is the unit tangential vector of the investigation of vanishing viscosity limit of solutions of the navier stokes equations both in the two and three spacial dimensional cases is a classical issue there are two related questions arising from here one is how to describe the inviscid limiting behavior of the navier stokes equation and the other is that does the euler equation can be approximated by the navier stokes equations in the case that the solution to the this research is supported in part by zheng ge ru foundation and hong kong rgc earmarked research grants cuhk 4028 04p cuhk 4040 02p and cuhk 4279 00p

on the regularity of flows with ladyzhenskaya shear dependent viscosity and slip or non slip boundary conditions navier stokes equations with shear dependent viscosity under the classical nonslip boundary condition were introduced and studied in the 1960s by o a ladyzhenskaya and in the case of gradient dependent viscosity by j l lions a particular case is the well known smagorinsky turbulence model this is nowadays a central subject of investigation on the other hand boundary conditions of slip type seems to be more realistic in some situations in particular in numerical applications they are a main research subject the existence of weak solutions u to the above problems with slip or nonslip type boundary conditions is well known in many cases however regularity up to the boundary still presents many open questions in what follows we present some regularity results in the stationary case for weak solutions to this kind of problem see theorem 3 1 and theorem 3 2 the evolution problem is studied in a forthcoming paper 6 a cornerstone in our proof is the classical nirenberg translation method see 38

slip with friction and penetration with resistance boundary conditions for the navier stokes equations numerical tests and aspects of the implementation we consider slip with friction and penetration with resistance boundary conditions in the steady state navier stokes equations this paper describes some aspects of the implementation of these boundary conditions for finite element discretizations numerical tests on two and three dimensional channel flows across a step using the slip with friction boundary condition study the influence of the friction parameter on the position of the reattachment point and the reattachment line of the recirculating vortex respectively

study of coating flow by the finite element method abstract silliman s analysis of slot coating is extended to accommodate film flows with highly bent menisci as in slide and curtain coating by combining polar and cartesian coordinate parametrizations of meniscus shape the nonlinear algebraic equations from the subdomain galerkin weighted residual method and finite element basis functions are solved by newton s method which is perfected for the free boundary problem convergence behavior is examined slot coating results reveal slow flow zones and show that at high capillary number and low metering rate the downstream meniscus can no longer attach to the slot comparison of coyne and elrod s approximate solutions with the finite element solutions shows that their assumption of a parabolic velocity profile leads to reasonable approximations of meniscus shapes

existence of weak solutions for steady viscous fluids with general slip boundary conditions abstract we study the existence of weak solutions for stationary viscous fluids with general slip boundary conditions in this paper applying monotone operator theory we first establish the existence result of weak solutions for an approximation problem then using the compactness methods and the point wise convergence property of velocity gradients we get the desired results

regularity criterion for generalized newtonian fluids in bounded domains abstract the regularity of a non newtonian flow in a domain with a boundary cannot be treated easily because of the nonlinear viscosity term and the global property of the pressure a distance function was used in a previous study to obtain a strong solution in the present study using the distance function idea we obtain serrin type regularity criteria for the vorticity and the velocity with regard to non newtonian equations with shear dependent viscosity in a bounded domain

a p q coupled system in elliptic nonlinear problems with nonstandard boundary conditions we state an abstract variational formulation to a coupled system constituted by an inequality and an equality motivated by the motion and energy equations and the constitutive laws for the stress tensor and the heat flux respectively when non newtonian fluids are taken care of here the existence of a weak solution is proven via a fixed point argument to multivalued mappings the nonstandard boundary conditions correspond to friction wall laws and energy transfer condition considered on a part of the boundary whereas there exists the presence of the frictional work due to the friction of the fluid motion we conclude by formulating the corresponding stationary heat conducting viscous incompressible flow problem and we establish an existence result

regularity of solutions to a non homogeneous boundary value problem for general stokes systems in r n we give a simple and very complete proof of the existence of a strong h2 solution to the non homogeneous problem 1 1 under the non homogeneous boundary conditions 1 6 here we consider the half space case rn n 3 see theorem 1 2 this regularity result was previously obtained by solonnikov and scadilov in reference 33 for the classical stokes system 0 g x 0 in the 3 d homogenous case a 0 b 0 and a suitable open subset of r3

penalty finite element method for stokes problem with nonlinear slip boundary conditions abstract the penalty finite element method for stokes problem with nonlinear slip boundary conditions based on the finite element subspace v h m h which satisfies the discrete inf sup condition is investigated in this paper since this class of nonlinear slip boundary conditions include the subdifferential property the weak variational formulation associated with stokes problem is variational inequality under some regularity assumptions we obtain the optimal h 1 and l 2 error estimates between u and u h and between u and u h e where the error orders are e h for h 1 error and e h 2 for l 2 error

optimal control of evolutionary quasi newtonian fluids we are interested in the necessary optimality conditions for optimal control problems of systems describing the unsteady flow of incompressible shear thickening fluids to overcome the difficulties related to the differentiability of the control to state mapping consequence of the lack of regularity of the state variable we first establish some intermediate optimality conditions and then pass to the limit

comparison between the homotopy perturbation method and the sine cosine wavelet method for solving linear integro differential equations this paper compares the homotopy perturbation method with the sine cosine wavelet method for solving linear integro differential equations from the computational viewpoint the homotopy perturbation method is more efficient and easier than the sine cosine wavelet method

on non newtonian p fluids the pseudo plastic case abstract in the following we study a class of stationary navier stokes equations with shear dependent viscosity under the non slip dirichlet boundary condition we consider pseudo plastic fluids a fluid is said pseudo plastic or shear thinning if in eq 1 1 below one has p 2 we are interested in global i e up to the boundary regularity results in dimension n 3 for the second order derivatives of the velocity and the first order derivatives of the pressure we consider a cubic domain and impose the non slip boundary condition only on two opposite faces on the other faces we assume periodicity as a device to avoid effective boundary conditions this choice is made so that we work in a bounded domain and simultaneously with a flat boundary

existence of the solution to stationary navier stokes equations with nonlinear slip boundary conditions abstract the stationary navier stokes equations with nonlinear slip boundary conditions are investigated in this paper because the boundary conditions include the subdifferential property on the part boundary the variational formulation of this problem is the variational inequality problem of the second kind with navier stokes operator the main purpose of the paper is to study the existence of the weak solution and the strong solution to this variational inequality problem in terms of the yosida s regularity method

a note on the regularity of flows with shear dependent viscosity abstract we consider a non newtonian fluid governed by stationary incompressible navier stokes equations with shear dependent viscosity using a fixed point argument in an appropriate functional setting we establish the existence of a strong solution for small and suitably regular data uniqueness results are obtained under similar conditions

finite element approximation of incompressible navier stokes equations with slip boundary condition we consider mixed finite element approximations of the stationary incompressible navier stokes equations with slip boundary condition simultaneously approximating the velocity pressure and normal stress component the stability of the schemes is achieved by adding suitable consistent penalty terms corresponding to the normal stress component and to the pressure a new method of proving the stability of the discretizations allows us to obtain optimal error estimates for the velocity pressure and normal stress component in natural norms without using duality arguments and without imposing uniformity conditions on the finite element partition the schemes can easily be implemented into existing finite element codes for the navier stokes equations with standard dirichlet boundary conditions

on the c1 γ ω w2 2 ω regularity for a class of electro rheological fluids abstract we are concerned with a system of nonlinear partial differential equations with p x structure 1 p p x p 0 and no slip boundary conditions we prove the existence and uniqueness of a c 1 w 2 2 solution corresponding to small data without further restrictions on the bounds p p 0 in particular this result is applicable to the steady motion of shear dependent electro rheological fluids