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We propose a mathematical model for fluids in multiphase flows in order to establish a solid theoretical foundation for the study of their complex topology, large geometric deformations, and topological changes such as merging. Our modeling…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
The full non-linear evolution of the tidal instability is studied numerically in an ellipsoidal fluid domain relevant for planetary cores applications. Our numerical model, based on a finite element method, is first validated by reproducing…
We investigate a system of nonlinear partial differential equations modeling the unsteady flow of a shear-thinning non-Newtonian fluid with a concentration-dependent power-law index. The system consists of the generalized Navier-Stokes…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
We study the out of equilibrium dynamics of several models exhibiting aging. We attempt at identifying various types of aging systems using a phase space point of view: we introduce a trial classification, based on the overlap between two…
We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…
This paper studies the upper bound of the lifespan of classical solutions of the initial value problems for one dimensional wave equations with quasilinear terms of space-, or time-derivatives of the unknown function. The results are same…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
We analyze asymptotically a differential-difference equation, that arises in a Markov-modulated fluid model. We use singular perturbation methods to analyze the problem with appropriate scalings of the two state variables. In particular,…
We discuss algorithms applicable to the numerical solution of second-order ordinary differential equations by finite-differences. We make particular reference to the solution of the dissipative particle dynamics fluid model, and present…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations.…
In this study, five different time-dependent incompressible non-Newtonian boundary layer models in two dimensions are investigated, including external magnetic field effects. The power law, the Casson fluid, the Oldroyd-B model, the Walter…
We investigate multidimensional model for incompressible non-Newtonian fluids. Using method of energy estimates we prove the property of finite speed of propagations of the solution support for this problem. We find sharp bounds of the…
By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on…
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting…
We are concerned with the energy equality for weak solutions to Newtonian and non-Newtonian incompressible fluids. In particular, the results obtained for non-Newtonian fluids, after restriction to the Newtonian case, equal or improve the…
This work presents a tentative discussion of certain aspects of energy behavior in the context of mathematical fluid dynamics. While some observations are made regarding certain patterns in energy behavior under particular conditions, the…