A singular perturbation problem in a system of nonlinear Schrödinger equation occurring in Langmuir turbulence
A singular perturbation problem in a system of nonlinear Schrödinger equation occurring in Langmuir turbulence
The aim of this work is to establish, from a mathematical point of view, the limit α → +∞ in the system where . This corresponds to an approximation which is made in the context of Langmuir turbulence in plasma Physics. The L2-subcritical σ (that is σ ≤ 2/3) and the H1-subcritical σ (that is σ ≤ 2) are studied. In the physical case σ = 1, the limit is then studied for the norm.
A singular radially symmetric problem in electrolytes theory
Existence of radially symmetric solutions (both stationary and time dependent) for a parabolic-elliptic system describing the evolution of the spatial density of ions in an electrolyte is studied.
A Singular Solution of the Capillary Equation. I. Existence.
A Singular Solution of the Capillary Equation. II. Uniqueness.
A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations
The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trustregion radius is defined by a Sobolev norm and the trust-region subproblems are solved by a dogleg method. Numerical test results show the method to be effective.
A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems
This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems. The reaction-diffusion...
A spectral Galerkin approximation of the Orr-Sommerfeld eigenvalue problem in a semi-finite domain.
A spectral perturbation problem and its applications to waves above an underwater ridge.
A spectral-Tau approximation for the Stokes and Navier-Stokes equations
A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations
In this paper we solve the time-dependent incompressible Navier-Stokes equations by splitting the non-linearity and incompressibility, and using discontinuous or continuous finite element methods in space. We prove optimal error estimates for the velocity and suboptimal estimates for the pressure. We present some numerical experiments.
A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations
In this paper we solve the time-dependent incompressible Navier-Stokes equations by splitting the non-linearity and incompressibility, and using discontinuous or continuous finite element methods in space. We prove optimal error estimates for the velocity and suboptimal estimates for the pressure. We present some numerical experiments.
A stability theorem of the Navier-Stokes flow past a rotating body
In this paper, a stability theorem of the Navier-Stokes flow past a rotating body is reported. Concerning the linearized problem, the proofs of the generation of a C₀ semigroup and its decay properties are sketched.
A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes
It is well known that the classical local projection method as well as residual-based stabilization techniques, as for instance streamline upwind Petrov-Galerkin (SUPG), are optimal on isotropic meshes. Here we extend the local projection stabilization for the Navier-Stokes system to anisotropic quadrilateral meshes in two spatial dimensions. We describe the new method and prove an a priori error estimate. This method leads on anisotropic meshes to qualitatively better convergence behavior...
A stabilized mixed finite element method for single-phase compressible flow.
A stable mixed finite element method on truncated exterior domains
A stationary flow of fresh and salt groundwater in a heterogeneous coastal aquifer
Si stabilisce l'esistenza e l'unicità di una soluzione monotona per il problema di frontiera libera correlato al flusso stazionare d'acqua dolce e salata intorno ad un acquifero eterogeneo. Si provano la continuità e l'esistenza di un limite asintotico della frontiera libera.
A steady-state capturing method for hyperbolic systems with geometrical source terms
We propose a simple numerical method for capturing the steady state solution of hyperbolic systems with geometrical source terms. We use the interface value, rather than the cell-averages, for the source terms that balance the nonlinear convection at the cell interface, allowing the numerical capturing of the steady state with a formal high order accuracy. This method applies to Godunov or Roe type upwind methods but requires no modification of the Riemann solver. Numerical experiments on scalar...
A steady-state capturing method for hyperbolic systems with geometrical source terms
We propose a simple numerical method for capturing the steady state solution of hyperbolic systems with geometrical source terms. We use the interface value, rather than the cell-averages, for the source terms that balance the nonlinear convection at the cell interface, allowing the numerical capturing of the steady state with a formal high order accuracy. This method applies to Godunov or Roe type upwind methods but requires no modification of the Riemann solver. Numerical experiments on scalar...
A stochastic lagrangian proof of global existence of the Navier-Stokes equations for flows with small Reynolds number