English

In the present paper, we study the combined incompressible and fast rotation limits for the full Navier-Stokes-Fourier system with Coriolis, centrifugal and gravitational forces, in the regime of small Mach, Froude and Rossby numbers and for general ill-prepared initial data. We consider both the isotropic scaling (where all the numbers have the same order of magnitude) and the multi-scale case (where some effect is predominant with respect to the others). In the case when the Mach number is of higher order than the Rossby number, we prove that the limit dynamics is described by an incompressible Oberbeck-Boussinesq system, where the velocity field is horizontal (according to the Taylor-Proudman theorem), but vertical effects on the temperature equation are not negligible. Instead, when the Mach and Rossby numbers have the same order of magnitude, and in absence of the centrifugal force, we show convergence to a quasi-geostrophic equation for a stream function of the limit velocity field, coupled with a transport-diffusion equation for a new unknown, which links the target density and temperature profiles. The proof of the convergence is based on a compensated compactness argument. The key point is to identify some compactness properties hidden in the system of acoustic-Poincar\'e waves. Compared to previous results, our method enables first of all to treat the whole range of parameters in the multi-scale problem, and also to consider a low Froude number regime with the somehow critical choice $Fr=\sqrt{Ma}$, where $Ma$ is the Mach number. This allows us to capture some (low) stratification effects in the limit.

In this paper, we investigate the combined nonequilibrium diffusion and low Mach number limits of the compressible Navier–Stokes–Fourier–P1 (NSF–P1) model with general initial data, which arises in the radiation hydrodynamics. Compared to the classical compressible Navier–Stokes–Fourier system, the NSF–P1 model has an asymmetric singular structure caused by the radiation field. To handle these singular terms, we introduce an equivalent pressure and an equivalent velocity to balance the order of singularity and establish the uniform estimates of solutions by designating appropriate weighted norms as well as carrying out delicate energy analysis. We conclude that, for partial general initial data and the strong scattering effect, the NSF–P1 model converges to the system of low Mach number heat‐conducting viscous flows coupled with a diffusion equation. We also discuss the variations of the limit equations as the scattering intensity changes. Furthermore, when the scattering effect is sufficiently weak, we can obtain the singular limits of the NSF–P1 model with full general initial data.

In this paper we consider the magnetohydrodynamics flows giving rise to a variety of mathematical problems in many areas. We study the incompressible limit problems for magnetohydrodynamics flows understrong stratification on unbounded domains.

This paper describes the study of flow behavior of the transonic compressor stage in un-stalled and stalled conditions. Experiments were carried out in an open circuit single stage transonic axial flow compressor test rig. The test compressor was designed for 1.35 total to total pressure ratio at corrected mass flow rate of 22 kg/s. Both steady and unsteady measurements were carried out. The operating envelop of the compressor was experimentally determined to demark the stable and unstable operating range of the compressor at different operating speeds. Variations in the rotor inlet axial and tangential velocity in the tip region were studied using a calibrated single component hot wire probe. The compressor blade element performance was obtained at full flow and near stall conditions using a three hole aerodynamic probe. The variation in flow parameters like absolute flow angle, axial Mach number, absolute Mach number, tangential Mach number, static and total pressure ratio profiles at the rotor exit were obtained and their variations along the blade height were studied at full flow and near stall conditions. Static pressure variation in the tip region along the rotor chord was studied which showed reduction in slope as stall approached. Hotwire measurements showed abrupt variation in the axial velocity as compared to tangential velocity at stalled condition. It was observed that the flow turned in tangential direction at stall, as tangential component of velocity shows more fluctuations at stall in comparison with unstalled condition. The FFT analysis of the raw signals was performed and it was observed that the nature of the rotating stall was abrupt and stall cell travels nearly at half the rotor speed.

In this paper, we investigate the low Mach and low Froude numbers limit for the compressible Navier–Stokes equations with degenerate, density-dependent, viscosity coefficient, in the strong stratification regime. We consider the case of a general pressure law with singular component close to vacuum, and general ill-prepared initial data. We perform our study in the three-dimensional periodic domain. We rigorously justify the convergence to the generalised anelastic approximation, which is used extensively to model atmospheric flows.

An initial–boundary-value problem for the nonlinear equations of real compressible viscous heat-conducting flow with general large initial data is investigated. The main point is to study the real flow for which the pressure and internal energy have nonlinear dependence on temperature, unlike the linear dependence for ideal flow, and the viscosity coefficients and heat conductivity are also functions of density and/or temperature. The shear viscosity is also presented. The existence, uniqueness and regularity of global solutions are established with large initial data in H1. It is shown that there is no shock wave, vacuum, mass concentration, or heat concentration (hot spots) developed in a finite time, although the solutions have large oscillations.

Asymptotic limits of the isentropic compressible viscous magnetohydrodynamic equations with Navier-slip boundary conditions

Unique solvability for the density-dependent Navier–Stokes equations

Hypersonic similarity for steady compressible full Euler flows over two-dimensional Lipschitz wedges

In this work, we are interested in the link between strong solutions of the Boltzmann and the Navier–Stokes equations. To justify this connection, our main idea is to use information on the limit system (for instance the fact that the Navier–Stokes equations are globally wellposed in two space dimensions or when the initial data is small). In particular we prove that the life span of the solutions to the rescaled Boltzmann equation is bounded from below by that of the Navier–Stokes system. We deal with general initial data in the whole space in dimensions 2 and 3, and also with well-prepared data in the case of periodic boundary conditions.

The present paper is devoted to the compressible nematic liquid crystal flow in the whole space $ \mathbb{R}^N\,(N≥ 2)$. Here we concentrate on the incompressible limit in the $ L^p$ type critical Besov spaces setting. We first establish the existence of global solutions in the framework of $ L^p$ type critical spaces provided that the initial data are close to some equilibrium states. Based on the global existence, we then consider the incompressible limit problem in the ill prepared data case. We justify the low Mach number convergence to the incompressible flow of liquid crystals in proper function spaces. In addition, the accurate converge rates are obtained.

On the incompressible and non-resistive limit of 3D compressible magnetohydrodynamic equations in bounded domains

We study the existence and uniqueness of non-negative solutions of the nonlinear parabolic equationposed inQ=RN× (0, ∞) with general initial datau(x, 0) =u0(x) ≧ 0. We find optimal exponential growth conditions for existence of solutions. Similar conditions apply for uniqueness, but the growth rate is different. Such conditions strongly depart from the linear casem= 1,ut= Δu–u, and also from the purely diffusive caseut= Δum.

Nous considérons l’équation de chaleur stochastique (SHE) de dimension (1+1) avec bruit blanc multiplicatif et la solution de Cole-Hopf de l’équation de Kardar–Parisi–Zhang. Nous montrons une manière exacte de calculer les exposants de Lyapunov du SHE pour une grande classe de données initiales qui inclut toutes les données initiales positives déterministes bornées et les données initiales stationnaires. En conséquence, nous déduisons des formules exactes pour les fonctions de taux de grande déviation de la queue supérieure de l’équation KPZ pour les données initiales générales.

On the semiclassical limit of the focusing nonlinear Schrödinger equation