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Antonin Novotny

Publications and source records attributed to Antonin Novotny.

33 records · Page 2Linked to original sources
arXiv2015

On the motion of viscous, compressible and heat-conducting liquids

We consider a system of equations governing the motion of a viscous, compressible, and heat conducting liquid-like fluid, with a general EOS of Mie-Grueneisen type. In addition, we suppose that the viscosity coefficients may decay to zero for large values of the temperature. We show the existence of global-in-time weak solution, derive a relative energy inequality, and compare the weak solutions with strong one emanating from the same initial data - the weak strong uniqueness property.

math.AP↗
arXiv2015

On singular limits arising in the scale analysis of stratified fluid flows

We study the low Mach low Freude numbers limit in the compressible Navier-Stokes equations and the transport equation for evolution of an entropy variable -- the potential temperature $Θ$. We consider the case of well-prepared initial data on "flat" tours and Reynolds number tending to infinity, and the case of ill-prepared data on an infinite slab. In both cases, we show that the weak solutions to the primitive system converge to the solution to the anelastic Navier-Stokes system and the transport equation for the second order variation of $Θ$

math.AP↗
arXiv2015

Error estimates for a numerical approximation to the compressible barotropic Navier-Stokes equations

We present here a general method based on the investigation of the relative energy of the system, that provides an unconditional error estimate for the approximate solution of the barotropic Navier Stokes equations obtained by time and space discretization. We use this methodology to derive an error estimate for a specific DG/finite element scheme for which the convergence was proved in [27]. This is an extended version of the paper submitted to IMAJNA.

math.NA↗
arXiv2014

Robustness of strong solutions to the compressible Navier-Stokes system

We consider the Navier-Stokes system describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier's slip boundary conditions. It is shown that the class of global in time strong solutions is robust with respect to small perturbations of the initial data. Explicit qualitative estimates are given also in terms of the shape of the underlying physical domain, with applications to problems posed on thin cylinders.

math.AP↗
arXiv2013

Inviscid incompressible limits under mild stratification: A rigorous derivation of the Euler-Boussinesq system

We consider the full Navier-Stokes-Fourier system in the singular regime of small Mach and large Reynolds and Peclet numbers, with ill prepared initial data on an unbounded domain in the three dimensional Euclidean space with a compact boundary. We perform the singular limit in the framework of weak solutions and identify the Euler-Boussinesq system as the target problem.

math.AP↗
arXiv2013

Multiple scales and singular limits for compressible rotating fluids with general initial data

We study the singular limit of a rotating compressible fluid described by a scaled barotropic Navier-Stokes system, where the Rossby number, the Mach number and the Froude number tend to 0 in a particular mutual rate while the Reynolds number tends to infinity. The inviscid planar Euler system is identified as the limit problem. The proof is based on the application of the method of relative entropies and careful analysis of oscillatory integrals describing the propagation of Rossby-acoustic waves.

math.AP↗
arXiv2013

Scale interactions in compressible rotating fluids

We study a triple singular limit for the scaled barotropic Navier-Stokes system modeling the motion of a rotating, compressible, and viscous fluid, where the Mach and Rossby numbers are proportional to a small parameter, while the Reynolds number becomes infinite. If the fluid is confined to an infinite slab bounded above and below by two parallel planes, the limit behavior is identified as a purely horizontal motion of an incompressible inviscid fluid, the evolution of which is described by an analogue of the Euler system.

math.AP↗
arXiv2012

Compressible fluid flows driven by stochastic forcing

We consider the Navier-Stokes system describing the motion of a compressible barotropic fluid driven by stochastic external forces. Our approach is semi-deterministic, based on solving the system for each fixed representative of the random variable and applying an abstract result on measurability of multi-valued maps. The class of admissible driving forces includes the (temporal) white noise and the random kicks, considered recently in the context of incompressible fluid models.

math.AP↗
arXiv2011

On the vanishing electron-mass limit in plasma hydrodynamics in unbounded media

We consider the zero-electron-mass limit for the Navier-Stokes-Poisson system in unbounded spatial domains. Assuming smallness of the viscosity coefficient and ill-prepared initial data, we show that the asymptotic limit is represented by the incompressible Navier-Stokes system, with a Brinkman damping, in the case when viscosity is proportional to the electron-mass, and by the incompressible Euler system provided the viscosity is dominated by the electron mass. The proof is based on the RAGE theorem and dispersive estimates for acoustic waves, and on the concept of suitable weak solutions for the compressible Navier-Stokes system.

math.AP↗
arXiv2011

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.

math.AP↗
arXiv2011

Multi-scale analysis of compressible viscous and rotating fluids

We study a singular limit for the compressible Navier-Stokes system when the Mach and Rossby numbers are proportional to certain powers of a small parameter $\ep$. If the Rossby number dominates the Mach number, the limit problem is represented by the 2-D incompressible Navier-Stokes system describing the horizontal motion of vertical averages of the velocity field. If they are of the same order then the limit problem turns out to be a linear, 2-D equation with a unique radially symmetric solution. The effect of the centrifugal force is taken into account.

math.AP↗
arXiv2010

A singular limit for compressible rotating fluids

We consider a singular limit problem for the Navier-Stokes system of a rotating compressible fluid, where the Rossby and Mach numbers tend simultaneously to zero. The limit problem is identified as the 2-D Navier-Stokes system in the ``horizontal'' variables containing an extra term that accounts for compressibility in the original system.

math.AP↗