On the vanishing viscosity approximation to the Cauchy problem for a 2 × 2 system of conservation laws
On the variational inequality approach to compressible flows via hodograph method.
We study the flow of a compressible, stationary and irrotational fluid with wake, in a channel, around a convex symmetric profile, with assigned velocity q-infinity at infinity and q-s < q-infinity at the wake. In particular, we study the regularity of the free boundary (for a problem which has non-constant coefficients), in the hodograph plane.
On the well-balance property of Roe’s method for nonconservative hyperbolic systems. Applications to shallow-water systems
This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys. 102 (1992) 360–373]. Next, this general theory is applied to obtain well-balanced...
On the well-balance property of Roe's method for nonconservative hyperbolic systems. applications to shallow-water systems
This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys.102 (1992) 360–373]. Next, this general theory is applied to obtain well-balanced...
On the asymptotic properties of solutions of the Navier-Stokes equations in the half-space.
On three-dimensional vortex patches
On two-dimensional and three dimensional axially-symmetric rotational flows of an ideal incompressible fluid
On uniqueness for bounded channel flows of viscoelastic fluids
It was conjectured in [1] that there is at most one bounded channel flow for a viscoelastic fluid whose stress relaxation function is positive, integrable, and strictly convex. In this paper we prove the uniqueness of bounded channel flows, assuming to be non-negative, integrable, and convex, but different from a very specific piecewise linear function. Furthermore, whenever these hypotheses apply, the unbounded channel flows, if any, must grow in time faster than any polynomial.
On Unsteady Boundary Layers In A Rotating Fluid With Time-Dependent Suction
On unsteady compressible laminar boundary layers past bodies of revolution spinning about its axis.
On unsteady three-dimensional boundary layer.
On unsteady two-phase fluid flow due to eccentric rotation of a disk.
On variational formulations for the Stokes equations with nonstandard boundary conditions
On various types of viscous two-fluid flows
Viscous two-fluid flows arise in different kinds of coating technologies. Frequently, the corresponding mathematical models represent two-dimensional free boundary value problems for the Navier-Stokes equations or their modifications. In this review article we present some results about nonisothermal stationary as well as about isothermal evolutionary viscous flow problems. The temperature-depending problems are characterized by coupled heat- and mass transfer and also by thermocapillary convection....
On viscous and resistive dissipation on Alfvén waves in an isothermal atmosphere.
On wave propagation and uniqueness in nonviscous fluid dynamics
On weak solutions of steady Navier-Stokes equations for monatomic gas
We use estimates for the inverse Laplacian of the pressure introduced by Plotnikov, Sokolowski and Frehse, Goj, Steinhauer together with the nonlinear potential theory due to Adams, Hedberg, to get a priori estimates and to prove existence of weak solutions to steady isentropic Navier-Stokes equations with the adiabatic constant for the flows powered by volume non-potential forces and with for the flows powered by potential forces and arbitrary non-volume forces. According to our knowledge,...
On weak solutions of the equations of motion of a viscoelastic medium with variable boundary.
On weak solutions to the equations of non-stationary motion of heat-conducting incompressible viscous fluids: defect measure and energy equality
We consider the non-stationary Navier-Stokes equations completed by the equation of conservation of internal energy. The viscosity of the fluid is assumed to depend on the temperature, and the dissipation term is the only heat source in the conservation of internal energy. For the system of PDE's under consideration, we prove the existence of a weak solution such that: 1) the weak form of the conservation of internal energy involves a defect measure, and 2) the equality for the total energy is satisfied....
On weak-strong uniqueness property for full compressible magnetohydrodynamics flows
This paper is devoted to the study of the weak-strong uniqueness property for full compressible magnetohydrodynamics flows. The governing equations for magnetohydrodynamic flows are expressed by the full Navier-Stokes system for compressible fluids enhanced by forces due to the presence of the magnetic field as well as the gravity and an additional equation which describes the evolution of the magnetic field. Using the relative entropy inequality, we prove that a weak solution coincides with the...