On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
We present the semi-conductor Boltzmann equation, which is time-reversible, and indicate that it can be formally derived by considering the large time and small perturbing potential limit in the Von-Neumann equation (time-reversible). We then rigorously compute the corresponding asymptotics in the case of the Von-Neumann equation on the Torus. We show that the limiting equation we obtain does not coincide with the physically realistic model. The former is indeed an equation of Boltzmann type, yet...
On the derivation of homogeneous hydrostatic equations
On the derivation of homogeneous hydrostatic equations
In this paper we study the derivation of homogeneous hydrostatic equations starting from 2D Euler equations, following for instance [2,9]. We give a convergence result for convex profiles and a divergence result for a particular inflexion profile.
On the derivation of the Gross-Pitaevskii equation
This article reflects in its content the talk the author gave at the XVII Congresso dellUnione Matematica Italiana, held in Milano, 8-13 September 2003. We review about some recent results on the problem of deriving the Gross-Pitaevskii equation in dimension one from the dynamics of a quantum system with a large number of identical bosons. We explain the motivations for some peculiar choices (shape of the interaction potential, scaling, initial datum). Open problems are pointed out and difficulties...
On the differential system governing flows in magnetic field with data in .
On the dimension of the attractor for a perturbed 3d Ladyzhenskaya model
We consider the so-called Ladyzhenskaya model of incompressible fluid, with an additional artificial smoothing term ɛΔ3. We establish the global existence, uniqueness, and regularity of solutions. Finally, we show that there exists an exponential attractor, whose dimension we estimate in terms of the relevant physical quantities, independently of ɛ > 0.
On the dimension of the pullback attractors for -Navier-Stokes equations.
On the Dirac delta as initial condition for nonlinear Schrödinger equations
On the double-well problem for Dirac operators
On the energy critical focusing non-linear wave equation
On the equation of a rotating film.
On the equations of ideal incompressible magneto-hydrodynamics
On the essential spectrum of many-particle pseudorelativistic Hamiltonians with permutational symmetry account.
On the Euler equations of incompressible perfect fluids
On the Euler equations with a singular external velocity field
On the evolution equations of viscous gaseous stars
On the existence and regularity of the solutions to the incompressible Navier-Stokes equations in presence of mass diffusion
This paper is devoted to the study of the incompressible Navier-Stokes equations with mass diffusion in a bounded domain in R³ with C³ boundary. We prove the existence of weak solutions, in the large, and the behavior of the solutions as the diffusion parameter λ → 0. Moreover, the existence of L²-strong solution, in the small, and in the large for small data, is proved. Asymptotic regularity (the regularity after a finite period) of a weak solution is studied. Finally, using the Dore-Venni theory,...
On the Existence and Uniqueness of Non-homogeneous Motions in Exterior Domains.
On the existence for the Cauchy-Neumann problem for the Stokes system in the -framework
The existence for the Cauchy-Neumann problem for the Stokes system in a bounded domain is proved in a class such that the velocity belongs to , where r > 3. The proof is divided into three steps. First, the existence of solutions is proved in a half-space for vanishing initial data by applying the Marcinkiewicz multiplier theorem. Next, we prove the existence of weak solutions in a bounded domain and then we regularize them. Finally, the problem with nonvanishing initial data is considered....