: Questions of existence and uniqueness of steady flows of viscoelastic fluids have thus far not been understood, even for slow flows perturbing rest. This paper provides an existence result for slow flows with no in- and outflow boundaries. The fluid is assumed to be described by constitutive equations of a differential nature. The method used to prove existence is constructive and in fact very close to procedures used in numerical calculations.

Existence of slow steady flows of viscoelastic fluids with differential constitutive equations

Elements of the Theory of Functions and Functional Analysis, Volume 1. Me and Normed Spaces.

The present article is devoted to examine the significance of double stratification in third grade stagnation point flow towards a radiative stretching cylinder. The stagnation point is discussed categorically. Analysis is scrutinized in the presence of Thermophoresis, Brownian diffusion, double stratification and heat source/sink. Suitable typical transformations are used to drive the system of ordinary differential equation. The governing system is subjected to optimal homotopy analysis method (OHAM) for convergent series solutions. The impact of pertinent fluid parameters on the velocity field, temperature distribution and concentration of the nanoparticles is shown graphically. Numerical data is compiled in tabulare form for skin friction, Nusselt and Sherwood numbers to analyze the variation caused by the present model and to see the impact for industrial and engineering point of view.

Significance of Double Stratification in Stagnation Point Flow of Third-Grade Fluid towards a Radiative Stretching Cylinder

The cerebral vasculature is made up of highly specialized structures that assure constant brain perfusion necessary to meet the very high demand for oxygen and glucose by neurons and glial cells. A dense, redundant network of arteries is spread over the entire pial surface from which penetrating arteries dive into the cortex to reach the neurovascular units. Besides providing blood to the brain parenchyma, cerebral arteries are key in the drainage of interstitial fluid (ISF) and solutes such as amyloid-beta. This occurs along the basement membranes surrounding vascular smooth muscle cells, toward leptomeningeal arteries and deep cervical lymph nodes. The dense microvasculature is made up of fine capillaries. Capillary walls contain pericytes that have contractile properties and are lined by a highly specialized blood-brain barrier that regulates the entry of solutes and ions and maintains the integrity of the composition of ISF. They are also important for the production of ISF. Capillaries drain into venules that course centrifugally toward the cortex to reach cortical veins and empty into dural venous sinuses. The walls of the venous sinuses are also home to meningeal lymphatic vessels that support the drainage of cerebrospinal fluid, although such pathways are still poorly understood. Damage to macro- and microvasculature will compromise cerebral perfusion, hamper the highly synchronized movement of neurofluids, and affect the drainage of waste products leading to neuronal and glial degeneration. This review will present vascular anatomy, their role in fluid dynamics, and a summary of how their dysfunction can lead to neurodegeneration.

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Cerebral Vessels: An Overview of Anatomy, Physiology, and Role in the Drainage of Fluids and Solutes

Development of renewable energy resources by green finance, volatility and risk: Empirical evidence from China

On a 3D model of non-isothermal flows in a pipeline network

We consider an optimal control problem for non-isothermal steady flows of low-concentrated aqueous polymer solutions in a bounded 3D domain. In this problem, the state functions are the flow velocity and the temperature, while the control function is the heat flux through a given part of the boundary of the flow domain. We obtain sufficient conditions for the existence of weak solutions that minimize a cost functional under a given bounded set of admissible controls. It is shown that the marginal function of the considered control system is lower semi-continuous and the optimal states operator generates a continuous branch in a suitable function space.

Optimal Boundary Control of the Boussinesq Approximation for Polymeric Fluids

Optimal boundary control of nonlinear-viscous fluid flows

We consider the initial-boundary value problem for a model of motion of aqueous polymer solutions in a bounded three-dimensional domain subject to the Navier slip boundary condition. We construct a global (in time) weak solution to this problem. Moreover, we establish some uniqueness results, assuming additional regularity for weak solutions. Copyright © 2017 John Wiley & Sons, Ltd.

Global solutions for a model of polymeric flows with wall slip

We study an optimal control problem for the mathematical model that describes steady non-isothermal creeping flows of an incompressible fluid through a locally Lipschitz bounded domain The control parameters are the pressure and the temperature on the in-flow and out-flow parts of the boundary of the flow domain We propose the weak formulation of the problem and prove the existence of weak solutions that minimize a given cost functional It is also shown that the marginal function of this control system is lower semi-continuous

https://www.mdpi.com/2311-5521/4/3/133/pdf

Evgenii S. Baranovskii

Papers

On a 3D model of non-isothermal flows in a pipeline network

Optimal Boundary Control of the Boussinesq Approximation for Polymeric Fluids

Optimal boundary control of nonlinear-viscous fluid flows

Global solutions for a model of polymeric flows with wall slip

Optimal Boundary Control of Non-Isothermal Viscous Fluid Flow