A new regularity criterion for the Navier-Stokes equations.
A new technique in constructing closed-form solutions for nonlinear PDEs appearing in fluid mechanics and gas dynamics.
A new two-dimensional shallow water model including pressure effects and slow varying bottom topography
The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional...
A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography
The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional...
A new -scheme algorithm and incompressible FEM for viscoelastic fluid flows
A nonconforming finite element method of upstream type applied to the stationary Navier-Stokes equation
A Nonconforming Finite Element Method to Compute the Spectrum of an Operator Relative to the Stability of a Plasma in Toroidal Geometry.
A nonlinear Schrödinger equation with magnetic field effect: solitary waves with internal rotation
A non-local theory of superfluidity
We will formulate a macroscopic theory of Superfluidity, using a particular constitutive equation of differential form which we will demonstrate to be equivalent to a non-local relation between the stress and the density.
A non-overlapping domain decomposition method for continuous-pressure mixed finite element approximations of the Stokes problem
This study is mainly dedicated to the development and analysis of non-overlapping domain decomposition methods for solving continuous-pressure finite element formulations of the Stokes problem. These methods have the following special features. By keeping the equations and unknowns unchanged at the cross points, that is, points shared by more than two subdomains, one can interpret them as iterative solvers of the actual discrete problem directly issued from the finite element scheme. In this way,...
A non-overlapping domain decomposition method for continuous-pressure mixed finite element approximations of the Stokes problem***
This study is mainly dedicated to the development and analysis of non-overlapping domain decomposition methods for solving continuous-pressure finite element formulations of the Stokes problem. These methods have the following special features. By keeping the equations and unknowns unchanged at the cross points, that is, points shared by more than two subdomains, one can interpret them as iterative solvers of the actual discrete problem directly issued from the finite element scheme. In this way,...
A Nonstandard Approach to the Uniqueness Problem for the Navier-Stokes Equations.
A note on a degenerate elliptic equation with applications for lakes and seas.
A Note on an Application of the Lasota-York Fixed Point Theorem in the Turbulent Transport Problem
We study a model of motion of a passive tracer particle in a turbulent flow that is strongly mixing in time variable. In [8] we have shown that there exists a probability measure equivalent to the underlying physical probability under which the quasi-Lagrangian velocity process, i.e. the velocity of the flow observed from the vintage point of the moving particle, is stationary and ergodic. As a consequence, we proved the existence of the mean of the quasi-Lagrangian velocity, the so-called Stokes...
A note on an unsteady flow of an Oldroyd-B fluid.
A note on asymptotic helix and quantum mechanical structure.
A note on critical times of quasilinear hyperbolic systems
In this paper the exact formula for the critical time of generating discontinuity (shock wave) in a solution of a quasilinear hyperbolic system is derived. The applicability of the formula in the engineering praxis is shown on one-dimensional equations of isentropic non-viscous compressible fluid flow.
A Note on Exterior Capillarity Problems.
A note on poroacoustic traveling waves under Darcy's law: Exact solutions
A mathematical analysis of poroacoustic traveling wave phenomena is presented. Assuming that the fluid phase satisfies the perfect gas law and that the drag offered by the porous matrix is described by Darcy's law, exact traveling wave solutions (TWS)s, as well as asymptotic/approximate expressions, are derived and examined. In particular, stability issues are addressed, shock and acceleration waves are shown to arise, and special/limiting cases are noted. Lastly, connections to other fields are...
A note on start-up, plane couette flow involving second-grade fluids.