Related papers: Analysis of a three-dimensional rapidly rotating c…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
We prove the existence of unique regular solutions of steady-state buoyancy-driven flows of viscous incompressible heat-conducting fluids in 3D open channels under mixed boundary conditions. The model takes into account the phenomena of the…
The Cauchy problem of the compressible Oldroyd-B model without damping mechanism in R^n$ with $n\ge2$ is considered. The lack of dissipation in density and stress tensor in the model is compensated by exploiting an intrinsic structure and…
The scientific community employs complicated multiphysics simulations to understand the physics in Solar, Stellar, and Interstellar media. These must be tested against known solutions to ensure their validity. Several well-known tests…
Major challenges of micro thermal machines are the thermal insulation and mechanical tolerance in the case of sliding piston. Switching from piston to membrane in microengines can alleviate the latest and lead to planar architectures.…
This paper presents a numerical study of three-dimensional laminar mixed convection within a liquid flowing on a horizontal channel heated uniformly from below. The upper surface is free and assumed to be flat. The coupled Navier-Stokes and…
We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme which treat the nonlinear term explicitly (backward differentiation formula with a one-leg method). Uniform bounds on…
A type-I model of non-isothermal multicomponent systems of gases describing mass diffusive and heat conductive phenomena is presented. The derivation of the model and a convergence result among thermomechanical theories in the smooth regime…
This paper treats topology optimization of natural convection problems. A simplified model is suggested to describe the flow of an incompressible fluid in steady state conditions, similar to Darcy's law for fluid flow in porous media. The…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
We explore the space of scalar-tensor theories containing two non-conformalmetrics, and find a discontinuity pointing to a "critical" cosmological solution. Due to the different maximal speeds of propagation for matter and gravity,the…
A non-equilibrium thermodynamics model able to analyze the combined effect of diffusion and adsorption in porous materials is proposed. The model considers the coupled dynamics of the diffusive phase, described by a diffusion type equation,…
We present an evaporation experiment in a single fluid layer. When latent heat associated to the evaporation is large enough, the heat flow through the free surface of the layer generates temperature gradients that can destabilize the…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
In this paper we study a coupled system modeling the movement of a deformable solid immersed in a fluid. For the solid we consider a given deformation that has to obey several physical constraints. The motion of the fluid is modeled by the…
We start with the compressible Oldroyd--B model derived in \cite{Barrett-Lu-Suli} ({\em J. W. Barrett, Y. Lu, E. S\"uli. Existence of large-data finite-energy global weak solutions to a compressible Oldroyd--B model. Comm. Math. Sci. 15…
In this paper we are interested with a strongly coupled system of partial differential equations that modelizes free convection in a two-dimensional bounded domain filled with a fluid saturated porous medium. This model is inspired by the…
We propose a model for three-dimensional solids on a mesoscopic scale with a statistical mechanical description of dislocation lines in thermal equilibrium. The model has a linearized rotational symmetry, which is broken by boundary…
We construct and study global solutions for the 3-dimensional incompressible MHD systems with arbitrary small viscosity. In particular, we provide a rigorous justification for the following dynamical phenomenon observed in many contexts:…