Related papers: Improved a priori bounds for thermal fluid equatio…
The equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and…
We study the energy balance for weak solutions of the three-dimensional compressible Navier--Stokes equations in a bounded domain. We establish an $L^p$-$L^q$ regularity conditions on the velocity field for the energy equality to hold,…
Thin viscous liquid films driven by capillarity are well described in the lubrication theory through the thin film equation. In this article, we present an analytical solution of this equation for a particular initial profile: a stepped…
We prove the local well-posedness of the 3D free-boundary incompressible ideal magnetohydrodynamics (MHD) equations with surface tension, which describe the motion of a perfect conducting fluid in an electromagnetic field. We adapt the…
Recent microfluidic experiments have explored the precise positioning of micron-sized particles in liquid environments via laser-induced thermoviscous flow. From micro-robotics to biology at the subcellular scale, this versatile technique…
A complete thermodynamical analysis for a binary mixture of viscous Korteweg fluids with two velocities and two temperatures is developed. The constitutive functions are allowed to depend on the diffusion velocity and the specific internal…
Some analogies between different nonequilibrium heat conduction models, particularly, random walk, discrete variable model, and Boltzmann transport equation with the single relaxation time approximation, have been discussed. We show that…
The Euler and Navier-Stokes equations both belong to a closed system of three transport equations, describing the particle number density N, the macroscopic velocity v and the temperature T. These sytems are complete, leaving no room for…
We study the large-time behavior of strong solutions to the one-dimensional, compressible Navier-Stokes system for a viscous and heat conducting ideal polytropic gas, when the viscosity is constant and the heat conductivity is proportional…
In the present paper we study the fast rotation limit for viscous incompressible fluids with variable density, whose motion is influenced by the Coriolis force. We restrict our analysis to two dimensional flows. In the case when the initial…
We derive a priori estimates for the compressible free-boundary Euler equations with surface tension in three spatial dimensions in the case of a liquid. These are estimates for local existence in Lagrangian coordinates when the initial…
A principle of maximum entropy is proposed in the context of viscous incompressible flow in Eulerian coordinates. The relative entropy functional, defined over the space of $L^2$ divergence-free velocity fields, is maximized relative to…
We consider a binary fluid mixture, which lies in the one-phase region near the demixing critical point, and study its transport through a capillary tube linking two large reservoirs. We assume that short-range interactions cause…
In this work we study the coupled system of partial and ordinary differential equations describing the interaction between a compressible isentropic viscous fluid and a rigid body moving freely inside the fluid. In particular the position…
Three-dimensional, compressible, magnetohydrodynamic turbulence of an isothermal, self-gravitating fluid is analyzed using two-point statistics in the asymptotic limit of large Reynolds numbers (both kinetic and magnetic). Following an…
A general thermodynamic treatment of dissipative relativistic fluids is introduced, where the temperature four vector is not parallel to the velocity field of the fluid. Generic stability and kinetic equilibrium points out a particular…
Thermal transport in classical fluids is analyzed in terms of a Higher-Order Generalized Hydrodynamics (or Mesoscopic Hydro-Thermodynamics), that is, depending on the evolution of the energy density and its fluxes of all orders. It is…
We introduce a natural notion of incompressibility for fluids governed by the relativistic Euler equations on a fixed background spacetime, and show that the resulting equations reduce to the incompressible Euler equations in the classical…
In this dissertation two-dimensional buoyancy-driven flows are investigated. While usually the Navier-Stokes equations are equipped with no-slip boundary conditions here we focus on the Navier-slip conditions that, depending on the system…
We study traveling wave solutions to the free boundary problem associated to a generalized Navier-Stokes Fourier system, which models a viscous, incompressible, heat-conducting fluid. The fluid is assumed to occupy a horizontally infinite…