90 research outputs found
Coupling to the continuous spectrum and HFB approximation
We propose a new method to solve the Hartree-Fock-Bogoliubov equations for weakly bound nuclei whose purpose is to improve the treatment of the continuum when a finite range two-body interaction is used. We replace the traditional expansion on a discrete harmonic oscillator basis by a mixed eigenfunction expansion associated with a potential that explicitely includes a continuous spectrum. We overcome the problem of continuous spectrum discretization by using a resonance expansion
Analysis of Oscillations and Defect Measures for the Quasineutral Limit in Plasma Physics
We perform a rigorous analysis of the quasineutral limit for a hydrodynamical
model of a viscous plasma represented by the Navier Stokes Poisson system in
. We show that as the velocity field strongly
converges towards an incompressible velocity vector field and the density
fluctuation weakly converges to zero. In general the limit
velocity field cannot be expected to satisfy the incompressible Navier Stokes
equation, indeed the presence of high frequency oscillations strongly affects
the quadratic nonlinearities and we have to take care of self interacting wave
packets. We shall provide a detailed mathematical description of the
convergence process by using microlocal defect measures and by developing an
explicit correctors analysis. Moreover we will be able to identify an explicit
pseudo parabolic pde satisfied by the leading correctors terms. Our results
include all the previous results in literature, in particular we show that the
formal limit holds rigorously in the case of well prepared data.Comment: Submitted pape
Exterior problem for the spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity
Weak-strong uniqueness property for the full Navier-Stokes-Fourier system
The Navier-Stokes-Fourier system describing the motion of a compressible,
viscous, and heat conducting fluid is known to possess global-in-time weak
solutions for any initial data of finite energy. We show that a weak solution
coincides with the strong solution, emanating from the same initial data, as
long as the latter exists. In particular, strong solutions are unique within
the class of weak solutions
Global solutions to the three-dimensional full compressible magnetohydrodynamic flows
The equations of the three-dimensional viscous, compressible, and heat
conducting magnetohydrodynamic flows are considered in a bounded domain. The
viscosity coefficients and heat conductivity can depend on the temperature. A
solution to the initial-boundary value problem is constructed through an
approximation scheme and a weak convergence method. The existence of a global
variational weak solution to the three-dimensional full magnetohydrodynamic
equations with large data is established
Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows
The three-dimensional equations of compressible magnetohydrodynamic
isentropic flows are considered. An initial-boundary value problem is studied
in a bounded domain with large data. The existence and large-time behavior of
global weak solutions are established through a three-level approximation,
energy estimates, and weak convergence for the adiabatic exponent
and constant viscosity coefficients
Weak and strong solutions of equations of compressible magnetohydrodynamics
International audienceThis article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions. Then, existence of strong solutions in the neighbourhood of equilibrium states is reviewed, in particular with the method of Kawashima and Shizuta. Finally, the special case of dimension one is highlighted : the use of Lagrangian coordinates gives a simpler system, which is solved by standard techniques
Logarithmic asymptotic behaviour of the renormalized G-convolution product in four-dimensional euclidean space
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