On the cauchy problem for a one‐dimensional full compressible non‐Newtonian fluids

This paper is concerned with global existence and asymptotic behavior of H¹ solutions to the Cauchy problem of one‐dimensional full non‐Newtonian fluids with the weighted small initial data. We then obtain the global existence of Hⁱ(i = 2,4) solutions and their asymptotic behavior for the system. Copyright © 2015 John Wiley & Sons, Ltd.     

Local strong solutions to a compressible non‐Newtonian fluid with density‐dependent viscosity

We consider the initial boundary problem for a compressible non‐Newtonian fluid with density‐dependent viscosity. The local existence of strong solution is established that is based on some compatibility condition. Moreover, it is also proved that the solutions are to blow up, and the maximum norm of velocity gradients controls the possible break down of the strong solutions. Copyright © 2016 John Wiley & Sons, Ltd.     

Global strong solutions for a class of compressible non‐Newtonian fluids with vacuum

We study a class of compressible non‐Newtonian fluids in one space dimension. We prove, by using iterative method, the global time existence and uniqueness of strong solutions provided that the initial data satisfy a compatibility condition and the initial density is small in its H¹‐norm. The main difficulty is due to the strong nonlinearity of the system and the initial vacuum. Copyright © 2010 John Wiley & Sons, Ltd.     

Unique solvability for the density‐dependent non‐Newtonian compressible fluids with vacuum

The paper is devoted to the existence and uniqueness of local solutions for the density‐dependent non‐Newtonian compressible fluids with vacuum in one‐dimensional bounded intervals. The important points in this paper are that the initial density may vanish in an open subset and the viscosity coefficient is nonlinearly dependent of density and shear rate.     

Approximation of the incompressible non‐Newtonian fluid equations by the artificial compressibility method

This paper studies the approximation of the non‐Newtonian fluid equations by the artificial compressibility method. We first introduce a family of perturbed compressible non‐Newtonian fluid equations (depending on a positive parameter ε) that approximates the incompressible equations as ε → 0⁺. Then, we prove the unique existence and convergence of solutions for the compressible equations to the solutions of the incompressible equations. Copyright © 2012 John Wiley & Sons, Ltd.     

Asymptotic behavior for the one‐dimensional pth power Newtonian fluid in unbounded domains

We consider the initial and initial‐boundary value problems for a one‐dimensional pth power Newtonian fluid in unbounded domains with general large initial data. We show that the specific volume and the temperature are bounded from below and above uniformly in time and space and that the global solution is asymptotically stable as the time tends to infinity. Copyright © 2015 John Wiley & Sons, Ltd.     

A mathematical model for the study of gliding motion of bacteria on a layer of non‐Newtonian slime

This paper is concerned with a mathematical hydrodynamical model of motility involving an undulating cell surface. The cell surface transmits stresses through a layer of exuded slime to the substratum. The slime is considered as a Johnson–Segalman fluid. A perturbation approach is used to find the analytic solution. Analytical expressions for the stream function, velocity, pressure gradient and pressure rise over a wavelength as well as the corresponding computational results are presented. The propulsive and lift forces and the power required for gliding propulsion have also been determined. The presented mechanism is found to generate a force for the propulsion of glider at a realistic speed and requires an output of power that is much less than the organism's metabolic rate of energy production. It is observed that unlike the Newtonian case of slime, the lift force is generated due to the Weissenberg number for non‐Newtonian slime, represented by the model of Johnson–Segalman fluid. It is also found that power required for translation in Johnson–Segalman fluid is reduced. Copyright © 2004 John Wiley & Sons, Ltd.     

On the small time asymptotics of stochastic non‐Newtonian fluids

In this paper, a small‐time large deviation principle for the stochastic non‐Newtonian fluids driven by multiplicative noise is proved. Copyright © 2016 John Wiley & Sons, Ltd.     

Exponential stability for a one‐dimensional compressible viscous micropolar fluid

In this paper, we consider one‐dimensional compressible viscous and heat‐conducting micropolar fluid, being in a thermodynamical sense perfect and polytropic. The homogenous boundary conditions for velocity, microrotation, and temperature are introduced. This problem has a global solution with a priori estimates independent of time; with the help of this result, we first prove the exponential stability of solution in (H¹(0,1))⁴, and then we establish the global existence and exponential stability of solutions in (H²(0,1))⁴ under the suitable assumptions for initial data. The results in this paper improve those previously related results. Copyright © 2015 John Wiley & Sons, Ltd.     

Unconditional non‐linear stability for a fluid of third grade

The thermal convection in a layer of a third grade fluid is investigated, with viscosity being a general function of temperature. We develop a non‐linear stability analysis and prove that unconditional non‐linear stability criterion is achieved using a natural energy approach. This shows that, in some sense, the equations for a fluid of third grade are preferable to those for a fluid of second grade or a dipolar fluid. Copyright © 2004 John Wiley & Sons, Ltd.     

Analytic solution of natural convection flow of a non‐newtonian fluid between two vertical flat plates by using decomposition method

An analysis has been performed to study the natural convection of a non‐Newtonian fluid between two infinite parallel vertical flat plates and the effects of the non‐Newtonian nature of fluid on the heat transfer are studied. The governing boundary layer and temperature equations for this problem are reduced to an ordinary form and are solved by Adomian decomposition method (ADM) and numerical method. Velocity and temperature profiles are shown graphically. The obtained results are valid for the whole solution domain with high accuracy. These methods can be easily extended to other linear and non‐linear equations and so can be found widely applicable in engineering and science. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1384–1395, 2010     

Interior local null controllability of one‐dimensional compressible flow near a constant steady state

We consider the one‐dimensional compressible Navier–Stokes equations with periodic boundary conditions, with initial conditions in a small neighborhood of a state of uniform density and uniform nonzero velocity. We prove that, with a control given only by a body force localized in a subinterval, we can steer the system to uniform density and velocity. Copyright © 2016 John Wiley & Sons, Ltd.     

Heat transfer and Couette flow of a chemically reacting non‐linear fluid

In this paper we study the flow and heat transfer in a chemically reacting non‐linear fluid between two long horizontal parallel flat plates that are at different temperatures. The top plate is sheared, whereas the bottom plate is fixed. The fluid is modeled as a generalized power‐law fluid whose viscosity is also assumed to be a function of the concentration. The effects of radiation are neglected. The equations are made dimensionless and the boundary value problem is solved numerically; the velocity and temperature profiles are obtained for various dimensionless numbers. Published in 2009 by John Wiley & Sons, Ltd.     

Hydromagnetic rotating flow of a fourth‐order fluid past a porous plate

The rotating flow in the presence of a magnetic field is a problem belonging to hydromagnetics and deserves to be more widely studied than it has been to date. In the non‐linear regime the literature is scarce. We develop the governing equations for the unsteady hydromagnetic rotating flow of a fourth‐order fluid past a porous plate. The steady flow is governed by a boundary value problem in which the order of differential equations is more than the number of available boundary conditions. It is shown that by augmenting the boundary conditions based on asymptotic structures at infinity it is possible to obtain numerical solutions of the nonlinear hydromagnetic equations. Effects of uniform suction or blowing past the porous plate, exerted magnetic field and rotation on the flow phenomena, especially on the boundary layer structure near the plate, are numerically analysed and discussed. The flow behaviours of the Newtonian fluid and second‐, third‐ and fourth‐order non‐Newtonian fluids are compared for the special flow problem, respectively. Copyright © 2004 John Wiley & Sons, Ltd.     

On uniqueness and time regularity of flows of power‐law like non‐Newtonian fluids

Large class of non‐Newtonian fluids can be characterized by index p, which gives the growth of the constitutively determined part of the Cauchy stress tensor. In this paper, the uniqueness and the time regularity of flows of these fluids in an open bounded three‐dimensional domain is established for subcritical ps, i.e. for p>11/5. Our method works for ‘all’ physically relevant boundary conditions, the Cauchy stress need not be potential and it may depend explicitly on spatial and time variable. As a simple consequence of time regularity, pressure can be introduced as an integrable function even for Dirichlet boundary conditions. Moreover, these results allow us to define a dynamical system corresponding to the problem and to establish the existence of an exponential attractor. Copyright © 2010 John Wiley & Sons, Ltd.     

Existence in non‐smooth domain for compressible liquid crystals

This paper is devoted to the existence of compressible liquid crystals system in non‐smooth domain. We are tempted to prove the convergence of solutions depending on that of corresponding spatial domains for liquid crystals equations of compressible flow. Copyright © 2012 John Wiley & Sons, Ltd.     

The stationary Stefan problem with convection governed by a non‐linear Darcy's law

We consider the bidimensional stationary Stefan problem with convection. The problem is governed by a coupled system involving a non‐linear Darcy's law and the energy balance equation with second member in L¹. We prove existence of at least one weak solution of the problem, using the penalty method and the Schauder fixed point principle. Copyright © 1999 John Wiley & Sons, Ltd.     

Global well‐posedness for free boundary problem of the Oldroyd‐B model fluid flow

In this paper, we prove the global well‐posedness of non‐Newtonian viscous fluid flow of the Oldroyd‐B model with free surface in a bounded domain of N‐dimensional Euclidean space . The assumption of the problem is that the initial data are small enough and orthogonal to rigid motions. Copyright © 2015 John Wiley & Sons, Ltd.     

Exponential stability in one‐dimensional non‐linear thermoelasticity with second sound

In this paper, we consider a one‐dimensional non‐linear system of thermoelasticity with second sound. We establish an exponential decay result for solutions with small ‘enough’ initial data. This work extends the result of Racke (Math. Methods Appl. Sci. 2002; 25 :409–441) to a more general situation. Copyright © 2004 John Wiley & Sons, Ltd.