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Eduard Feireisl - One of the best experts on this subject based on the ideXlab platform.

  • Recent Progress in the Mathematical Theory of Viscous Compressible Fluids
    Mathematical Fluid Mechanics, 2020
    Co-Authors: Eduard Feireisl
    Abstract:

    We review some recent results on a priori estimates, compactness, global existence, and the long-time behaviour of solutions to the Navier-Stokes equations of a Compressible fluid flow.

  • on a singular limit for stratified Compressible Fluids
    Nonlinear Analysis-real World Applications, 2018
    Co-Authors: Eduard Feireisl, Gabriele Bruell
    Abstract:

    Abstract We consider a singular limit problem for the complete Compressible Euler system in the low Mach and strong stratification regime. We identify the limit problem – the anelastic Euler system – in the case of well prepared initial data. The result holds in the large class of the dissipative measure-valued solutions of the primitive system. Applications are discussed to the driven shallow water equations.

  • InCompressible Limit for Compressible Fluids with Stochastic Forcing
    Archive for Rational Mechanics and Analysis, 2016
    Co-Authors: Dominic Breit, Eduard Feireisl, Martina Hofmanova
    Abstract:

    We study the asymptotic behavior of the isentropic Navier–Stokes system driven by a multiplicative stochastic forcing in the Compressible regime, where the Mach number approaches zero. Our approach is based on the recently developed concept of a weak martingale solution to the primitive system, uniform bounds derived from a stochastic analogue of the modulated energy inequality, and careful analysis of acoustic waves. A stochastic inCompressible Navier–Stokes system is identified as the limit problem.

  • global weak solutions to a class of non newtonian Compressible Fluids
    Mathematical Methods in The Applied Sciences, 2015
    Co-Authors: Eduard Feireisl, Xian Liao, Josef Malek
    Abstract:

    We consider a class of Compressible Fluids with nonlinear constitutive equations that guarantee that the divergence of the velocity field remains bounded. We study mathematical properties of unsteady three-dimensional flows of such Fluids in bounded domains. In particular, we show the long-time and large-data existence result of weak solutions with strictly positive density. Copyright © 2015 John Wiley & Sons, Ltd.

  • analysis of a phase field model for two phase Compressible Fluids
    Mathematical Models and Methods in Applied Sciences, 2010
    Co-Authors: Eduard Feireisl, Hana Petzeltova, Elisabetta Rocca, Giulio Schimperna
    Abstract:

    A model describing the evolution of a binary mixture of Compressible, viscous, and macroscopically immiscible Fluids is investigated. The existence of global-in-time weak solutions for the resulting system coupling the Compressible Navier–Stokes equations governing the motion of the mixture with the Allen–Cahn equation for the order parameter is proved without any restriction on the size of initial data.

Oleg A. Godin - One of the best experts on this subject based on the ideXlab platform.

  • Shear waves in inhomogeneous, Compressible Fluids in a gravity field
    Journal of the Acoustical Society of America, 2014
    Co-Authors: Oleg A. Godin
    Abstract:

    While elastic solids support compressional and shear waves, waves in ideal Compressible Fluids are usually thought of as compressional waves. Here, a class of acoustic-gravity waves is studied in which the dilatation is identically zero, and the pressure and density remain constant in each fluid particle. These shear waves are described by an exact analytic solution of linearized hydrodynamics equations in inhomogeneous, quiescent, inviscid, Compressible Fluids with piecewise continuous parameters in a uniform gravity field. It is demonstrated that the shear acoustic-gravity waves also can be supported by moving Fluids as well as quiescent, viscous Fluids with and without thermal conductivity. Excitation of a shear-wave normal mode by a point source and the normal mode distortion in realistic environmental models are considered. The shear acoustic-gravity waves are likely to play a significant role in coupling wave processes in the ocean and atmosphere.

  • Shear waves in inviscid Compressible Fluids
    Journal of the Acoustical Society of America, 2013
    Co-Authors: Oleg A. Godin
    Abstract:

    While elastic solids support compressional and shear waves, waves in ideal Compressible Fluids are usually thought of as compressional waves. Here, a class of acoustic-gravity waves is studied in which the dilatation is identically zero, and the pressure and density remain constant in each fluid particle. An exact analytic solution of linearized hydrodynamics equations is obtained that describes the shear waves in inhomogeneous, inviscid, Compressible Fluids with piece-wise continuous parameters in a uniform gravity field. The solution is valid under surprisingly general assumptions about the environment and reduces to some classical wave types in appropriate limiting cases. Free shear waves in bounded and unbounded domains as well as excitation of the shear waves by a point source are considered. Edge waves propagating along vertical and inclined rigid boundaries are found in rotating and non-rotating Fluids. A possible role of the shear acoustic-gravity waves in a coupled ocean-atmosphere system is disc...

  • inCompressible wave motion of Compressible Fluids
    Physical Review Letters, 2012
    Co-Authors: Oleg A. Godin
    Abstract:

    : We consider linear waves in Compressible Fluids in a uniform potential field, such as a gravity field, and demonstrate that a particular type of wave motion, in which pressure remains constant in each fluid parcel, is supported by inhomogeneous Fluids occupying bounded or unbounded domains. We present elementary, exact solutions of linearized hydrodynamics equations, which describe the new type of waves in the coupled ocean-atmosphere system. The solutions provide an extension of surface gravity waves in an inCompressible fluid half-space with a free boundary to waves in Compressible, three-dimensionally inhomogeneous, rotating Fluids.

Daniel Livescu - One of the best experts on this subject based on the ideXlab platform.

  • rayleigh taylor instability in cylindrical geometry with Compressible Fluids
    Physics of Fluids, 2008
    Co-Authors: Huidan Yu, Daniel Livescu
    Abstract:

    A linear stability analysis of the Rayleigh–Taylor instability (RTI) between two ideal inviscid immiscible Compressible Fluids in cylindrical geometry is performed. Three-dimensional (3D) cylindrical as well as two-dimensional (2D) axisymmetric and circular unperturbed interfaces are considered and compared to the Cartesian cases with planar interface. Focuses are on the effects of compressibility, geometry, and differences between the convergent (gravity acting inward) and divergent (gravity acting outward) cases on the early instability growth. Compressibility can be characterized by two independent parameters—a static Mach number based on the isothermal sound speed and the ratio of specific heats. For a steady initial unperturbed state, these have opposite influence, stabilization and destabilization, on the instability growth, similar to the Cartesian case [D. Livescu, Phys. Fluids 16, 118 (2004)]. The instability is found to grow faster in the 3D cylindrical than in the Cartesian case in the converge...

Konstantina Trivisa - One of the best experts on this subject based on the ideXlab platform.

  • the stochastic navier stokes equations for heat conducting Compressible Fluids global existence of weak solutions
    Journal of Evolution Equations, 2018
    Co-Authors: Scott A Smith, Konstantina Trivisa
    Abstract:

    We investigate the well posedness of the stochastic Navier–Stokes equations for viscous, Compressible, non-isentropic Fluids. The global existence of finite-energy weak martingale solutions for large initial data within a bounded domain of \(\mathbb {R}^d\) is established under the condition that the adiabatic exponent \(\gamma > d/2.\) The flow is driven by a stochastic forcing of multiplicative type, white in time and colored in space. This work extends recent results on the isentropic case, the main contribution being to address the issues which arise from coupling with the temperature equation. The notion of solution and corresponding compactness analysis can be viewed as a stochastic counterpart to the work of Feireisl (Dynamics of viscous Compressible Fluids, vol 26. Oxford University Press, Oxford, 2004).

  • On a free boundary problem for polymeric Fluids: global existence of weak solutions
    Nonlinear Differential Equations and Applications NoDEA, 2017
    Co-Authors: Donatella Donatelli, Konstantina Trivisa
    Abstract:

    We investigate the stability and global existence of weak solutions to a free boundary problem governing the evolution of polymeric Fluids. We construct weak solutions of the two-phase model by performing the asymptotic limit of a macroscopic model governing the suspensions of rod-like molecules (known as Doi-model) in Compressible Fluids as the adiabatic exponent $$\gamma $$ γ goes to $$\infty .$$ ∞ . The convergence of these solutions, up to a subsequence, to the free-boundary problem is established using techniques in the spirit of Lions and Masmoudi (Ann Inst Henri Poincaré 16:373–410, 1999 ).

  • a multidimensional model for the combustion of Compressible Fluids
    Archive for Rational Mechanics and Analysis, 2007
    Co-Authors: Donatella Donatelli, Konstantina Trivisa
    Abstract:

    We consider a multidimensional model for the combustion of Compressible reacting Fluids. The flow is governed by the Navier–Stokes in Eulerian coordinates and the chemical reaction is irreversible and is governed by the Arrhenius kinetics. The existence of globally defined weak solutions is established by using weak convergence methods, compactness and interpolation arguments in the spirit of Feireisl [16] and P.L. Lions [24].

  • on the navier stokes equations for exothermically reacting Compressible Fluids
    Acta Mathematicae Applicatae Sinica, 2002
    Co-Authors: Guiqiang Chen, Konstantina Trivisa
    Abstract:

    We analyze mathematical models governing planar flow of chemical reaction from unburnt gases to burnt gases in certain physical regimes in which diffusive effects such as viscosity and heat conduction are significant. These models can be then formulated as the Navier-Stokes equations for exothermically reacting Compressible Fluids. We first establish the existence and dynamic behavior, including stability, regularity, and large-time behavior, of global discontinuous solutions of large oscillation to the Navier-Stokes equations with constant adiabatic exponent γ and specific heat cv. Our approach for the existence and regularity is to combine the difference approximation techniques with the energy methods, total variation estimates, and weak conver- gence arguments to deal with large jump discontinuities; and for large-time behavior is an a posteriori argument directly from the weak form of the equations. The approach and ideas we develop here can be applied to solving a more complicated model where γ and cv vary as the phase changes; and we then describe this model in detail and contrast the results on the asymptotic behavior of the solutions of these two different models. We also discuss other physical models describing dynamic combustion.

Heinrich Freistuhler - One of the best experts on this subject based on the ideXlab platform.

  • phase transitions and traveling waves in Compressible Fluids
    Archive for Rational Mechanics and Analysis, 2014
    Co-Authors: Heinrich Freistuhler
    Abstract:

    This note studies families of isothermal Navier–Stokes–Allen–Cahn systems that are parameterized by temperature. It shows that under natural assumptions, the possibility of traveling waves corresponding to phase boundaries arises during a phase transition at a critical temperature. Below that temperature, besides pairs of “Maxwell” states connected by waves with zero net mass flux, there exist also interfaces across which particles undergo a phase transformation.