Foreword [Proceedings of the Eighth International School on Mathematical Theory in Fluid Mechanics in memory of Professor Jindřich Nečas]
Formal passage from kinetic theory to incompressible Navier–Stokes equations for a mixture of gases
We present in this paper the formal passage from a kinetic model to the incompressible Navier−Stokes equations for a mixture of monoatomic gases with different masses. The starting point of this derivation is the collection of coupled Boltzmann equations for the mixture of gases. The diffusion coefficients for the concentrations of the species, as well as the ones appearing in the equations for velocity and temperature, are explicitly computed under the Maxwell molecule assumption in terms of the...
Formation of singularities for viscosity solutions of Hamilton-Jacobi equations
Fourier-Chebyshev pseudospectral method for two-dimensional vorticity equation.
Fourier-Chebyshev pseudospectral methods for the two-dimensional Navier-Stokes equations
Free boundary eigenfunctions for a nonlinear degenerate eigenvalue problem.
Free boundary problem for the equations of magnetohydrodynamic incompressible viscous fluid
The existence of a global motion of magnetohydrodynamic fluid in a domain bounded by a free surface and under the external electrodynamic field is proved. The motion is such that the velocity and magnetic field are small in the H³-space.
Free boundary problems and transonic shocks for the Euler equations in unbounded domains
We establish the existence and stability of multidimensional transonic shocks (hyperbolic-elliptic shocks), which are not nearly orthogonal to the flow direction, for the Euler equations for steady compressible potential fluids in unbounded domains in . The Euler equations can be written as a second order nonlinear equation of mixed hyperbolic-elliptic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the...
Free boundary problems for nonstationary Navier-Stokes equations [Book]
Free boundary problems for Stoke's flows and finite element methods
Free boundary problems in fluid dynamics
Free convection flow of conducting micropolar fluid with thermal relaxation including heat sources.
Free convection flow of water at past an infinite porous plate with constant suction
Free convective flow of a stratified fluid through a porous medium bounded by a vertical plane.
Free surface flow over an obstacle. Theoretical study of the fluvial case.
Free-energy-dissipative schemes for the Oldroyd-B model
In this article, we analyze the stability of various numerical schemes for differential models of viscoelastic fluids. More precisely, we consider the prototypical Oldroyd-B model, for which a free energy dissipation holds, and we show under which assumptions such a dissipation is also satisfied for the numerical scheme. Among the numerical schemes we analyze, we consider some discretizations based on the log-formulation of the Oldroyd-B system proposed by Fattal and Kupferman in [J. Non-Newtonian...
From discrete Boltzmann equation to compressible linearized Euler equations.
From the BGK model to the Navier–Stokes equations
Fronts de combustion en magnétohydrodynamique relativiste
Full regularity of weak solutions to a class of nonlinear fluids in two dimensions -- stationary, periodic problem
We prove the existence of regular solution to a system of nonlinear equations describing the steady motions of a certain class of non-Newtonian fluids in two dimensions. The equations are completed by requirement that all functions are periodic.