1,721,007 research outputs found
On the artificial compressibility method for the Navier Stokes Fourier system
No full textThis paper deals with the artificial compressibility approximation method adapted to the incompressible Navier Stokes Fourier system. Two different types of approximations will be analyzed: one for the full Navier Stokes Fourier system (or the so-called Rayleigh-Benard equations) where viscous heating effects are considered and the other for when the dissipative function S : ∇u is omitted. The convergence of the approximating sequences is achieved by exploiting the dispersive properties of the wave equation structure of the pressure of the approximating system
The artificial compressibility approximation for MHD equations in unbounded domain
No full textIn this paper we analyze a method of to approximation for the weak solutions of the incompressible magnetohydrodynamic equations (MHD) in unbounded domains. In particular we describe an hyperbolic version of the so called artificial compressibility method adapted to the MHD system. By exploiting the wave equation structure of the approximating system we achieve the convergence of the approximating sequences by means of dispersive estimate of Strichartz type. We prove that the soleinoidal component of the approximating velocity and magnetic fields is relatively compact and converges strongly to a weak solution of the MHD equation
On a Nonlinear Model for Tumor Growth: Global in Time Weak Solutions
No full textWe investigate the dynamics of a class of tumor growth models known as mixed models. The key characteristic of these type of tumor growth models is that the different populations of cells are continuously present everywhere in the tumor at all times. In this work we focus on the evolution of tumor growth in the presence of proliferating, quiescent and dead cells as well as a nutrient. The system is given by a multi-phase flow model and the tumor is described as a growing continuum Ω with boundary ∂Ω both of which evolve in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior, diffusion and viscosity in the weak formulation
Quasineutral limit, dispersion and oscillations for Korteweg type fluids
No full textIn the setting of general initial data and whole space we perform a rigorous analysis of the quasineutral limit for a hydrodynamical model of a viscous plasma with capillarity tensor represented by the Navier Stokes Korteweg Poisson system. We shall provide a detailed mathematical description of the convergence process by analyzing the dispersion of the fast oscillating acoustic waves. However the standard acoustic wave analysis is not sufficient to control the high frequency oscillations in the electric field but it is necessary to estimates the dispersive properties induced by the capillarity terms. Therefore by using these additional estimates we will be able to control, via compensated compactness, the quadratic nonlinearity of the stiff electric force field. In conclusion, opposite to the zero capillarity case \cite{DM12} where persistent space localized time high frequency oscillations need to be taken into account, we show that as \la\to 0, the density fluctuation \rl-1 converges strongly to zero and the fluids behaves according to an incompressible dynamics.In the setting of general initial data and the whole space we perform a rigorous analysis of the quasi-neutral limit for a hydrodynamical model of a viscous plasma with capillarity tensor represented by the Navier-Stokes-Poisson-Korteweg system. We shall provide a detailed mathematical description of the convergence process by analyzing the dispersion of the fast oscillating acoustic waves. However the standard acoustic wave analysis is not sufficient to control the high frequency oscillations in the electric field but it is necessary to estimates the dispersive properties induced by the capillarity terms. Therefore by using these additional estimates we will be able to control, via compensated compactness, the quadratic nonlinearity of the stiff electric force field. In conclusion, opposite to the zero capillarity case [D. Donatelli and P. Marcati, Arch. Ration. Mech. Anal., 206 (2012), pp. 159-188] where persistent space localized time high frequency oscillations need to be taken into account, we show that as λ → 0, the density fluctuation λ - 1 converges strongly to zero and the fluids behave according to an incompressible dynamics
On the motion of a viscous compressible radiative-reacting gas
No full textA multidimensional model is introduced for the dynamic combustion of compressible, radiative and reactive gases. In the macroscopic description adopted here, the radiation is treated as a continuous field, taking into account both the wave (classical) and photonic (quantum) aspects associated with the gas [20, 36]. The model is formulated by the Navier-Stokes equations in Euler coordinates, which is now expressed by the conservation of mass, the balance of momentum and energy and the two species chemical kinetics equation. In this context, we are dealing with a one way irreversible chemical reaction governed by a very general Arrhenius-type kinetics law. The analysis in the present article extends the earlier work of the authors [17], since it now covers the general situation where, both the heat conductivity and the viscosity depend on the temperature, the pressure now depends not only on the density and temperature but also on the mass fraction of the reactant, while the two species chemical kinetics equation is of higher order. The existence of globally defined weak solutions of the Navier-Stokes equations for compressible reacting fluids is established by using weak convergence methods, compactness and interpolation arguments in the spirit of Feireisl [26] and P.L. Lions [35]
An anelastic approximation arising in astrophysics
No full textWe identify the asymptotic limit of the compressible non-isentropic Navier– Stokes system in the regime of low Mach, low Froude and high Reynolds number. The system is driven by a long range gravitational potential. We show convergence to an anelastic system for ill-prepared initial data. The proof is based on frequency localized Strichartz estimates for the acoustic equation based on the recent work of Metcalfe and Tataru
Vanishing dielectric constant regime for the Navier Stokes Maxwell equations
No full textIn this paper we rigorously justify the convergence of smooth solutions of the Navier-Stokes-Maxwell equations towards smooth solutions of the classical 2D parabolic MHD equations in the case of vanishing dielectric constant. The result is achieved by means of higher-order energy estimates
1- D Relaxation from hyperbolic to parabolic systems with variable coefficients
No full textIn this paper we study the relaxation of semilinear hyperbolic systems to parabolic sys- tem. The singular limits are studied using G ́erard’s generalized compensated compactness
Leray weak solutions of the incompressible Navier Stokes system on exterior domains via the artificial compressibility method
No full textIn this paper we study the Leray weak solutions of the incompressible Navier Stokes equation in an exterior do- main. We describe, in particular, a hyperbolic version of the so called artificial compressibility method investigated by J.L. Lions and Temam. The convergence of these type of approx- imations shows in general a lack of strong convergence due to the presence of acoustic waves. In this paper we face this diffi- culty by taking care of the dispersive nature of these waves by means of the Strichartz estimates or waves equations satisfied by the pressure. We introduce wave equations to take care of the pressure in different acoustic components, each one of them satisfying a specific initial boundary value problem. The strong convergence analysis of the velocity field will be achieved by us- ing the associated Leray-Hodge decomposition
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