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We consider the initial-boundary value problem for the system of equations describing the flow of compressible isothermal mixture of arbitrary large number of components. The system consists of the compressible Navier-Stokes equations and a…
This article deals with the issues of global-in-time existence and asymptotic analysis of a fluid-particle interaction model in the so-called bubbling regime. The mixture occupies the physical space $\Omega \subset \mathbb{R}^3$ which may…
We study the global existence of solutions reaction-diffusion systems with control of mass on multiple domains. Some of these domains overlap, and as a result, an unknown defined on one subdomain can impact another unknown defined on a…
The LIT approach is reviewed both for inclusive and exclusive reactions. It is shown that the method reduces a continuum state problem to a bound-state-like problem, which then can be solved with typical bound-state techniques. The LIT…
A complex non-Newtonian fluid models the nematic liquid crystal flows confined in a bounded domain in $\mathbb{R}^3$ is considered. The system is a forced incompressible Navier-Stokes equation coupled with a parabolic type Q-tensor flows.…
A reaction--diffusion replicator equation is studied. A novel method to apply the principle of global regulation is used to write down the model with explicit spatial structure. Properties of stationary solutions together with their…
The equations for the three-dimensional incompressible flow of liquid crystals are considered in a smooth bounded domain. The existence and uniqueness of the global strong solution with small initial data are established. It is also proved…
A class of solutions, decaying as $t\rightarrow \infty$, of a two-dimensional model problem on the oscillations of an ideal rotating fluid in some domains with angular points is constructed explicitly. The existence of solutions whose…
We introduce many families of explicit solutions to the three dimensional incompressible Euler equations for nonviscous fluid flows using the Lagrangian framework. Almost no exact Lagrangian solutions exist in the literature prior to this…
The author studies the flows of an ideal incompressible fluid in a 2-dimensional domain, and in particular questions of instability and controllability.
The development of high-efficiency porous catalyst membranes critically depends on our understanding of where the majority of the chemical conversions occur within the porous structure. This requires mapping of chemical reactions and mass…
This paper considers quadratic and super-quadratic reaction-diffusion systems for reversible chemistry, for which all species satisfy uniform-in-time $L^1$ a-priori estimates, for instance, as a consequence of suitable mass conservation…
A study of regularity estimate for weak solution to generalized stationary Stokes-type systems involving $p$-Laplacian is offered. The governing systems of equations are based on steady incompressible flow of a Newtonian fluids. This paper…
Steady flows of an incompressible homogeneous chemically reacting fluid are described by a coupled system, consisting of the generalized Navier--Stokes equations and convection - diffusion equation with diffusivity dependent on the…
Binary fluid mixtures are examples of complex fluids whose microstructure and flow are strongly coupled. For pairs of simple fluids, the microstructure consists of droplets or bicontinuous demixed domains and the physics is controlled by…
This investigation deals with some exact solutions of the equations governing the steady plane motions of an incompressible third grade fluid by using complex variables and complex functions. Some of the solutions admit, as particular…
For many real physico-chemical complex systems detailed mechanism includes both reversible and irreversible reactions. Such systems are typical in homogeneous combustion and heterogeneous catalytic oxidation. Most complex enzyme reactions…
Hydrodynamic equations for ideal incompressible fluid are written in terms of generalized stream function. Two-dimensional version of these equations is transformed to the form of one dynamic equation for the stream function. This equation…
MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock-bubble interaction, and gas bubble…
Phase separation is the thermodynamic process that explains how droplets form in multicomponent fluids. These droplets can provide controlled compartments to localize chemical reactions, and reactions can also affect the droplets' dynamics.…