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Sarka Necasova

Publications and source records attributed to Sarka Necasova.

31 records · Page 2Linked to original sources
arXiv2019

Artificial boundary conditions for linearized stationary incompressible viscous flow around rotating and translating body

We consider the linearized and nonlinear stationary incompressible flow around rotating and translating body in the exterior domain B with Lipschitz boundary. We derive the pointwise estimates for the pressure in both cases. Moreover, we consider the linearized problem in a truncation domain B_R of the exterior domain B under certain artificial boundary conditions on the truncating boundary and then compare this solution with the solution in the exterior domain B to get the truncation error estimate.

math.AP↗
arXiv2019

Low Mach number limit on thin domains

We consider the compressible Navier-Stokes system describing the motion of a viscous fluid confined to a straight layer $Ω_δ=(0,δ)\times\mathbb{R}^2$. We show that the weak solutions in the 3D domain converge strongly to the solution of the 2D incompressible Navier-Stokes equations (Euler equations) when the Mach number $ε$ tends to zero as well as $δ\rightarrow 0$ (and the viscosity goes to zero).

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arXiv2019

Weak-strong uniqueness for the compressible fluid-rigid body interaction

In this work we study the coupled system of partial and ordinary differential equations describing the interaction between a compressible isentropic viscous fluid and a rigid body moving freely inside the fluid. In particular the position and velocity of the rigid body in the fluid are unknown and the motion of the rigid body is driven by the normal stress forces of the fluid acting on the boundary of the body. We prove that the strong solution, which is known to exist under certain smallness assumptions, is unique in the class of weak solutions to the problem. The proof relies on a correct definition of the relative energy, to use this tool we then have to introduce a change of coordinates to transform the strong solution to the domain of the weak solution in order to use it as a test function in the relative energy inequality. Estimating all arising terms we prove that the weak solution has to coincide with the transformed strong solution and finally that the transformation has to be in fact an identity.

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arXiv2018

Weak-strong uniqueness for fluid-rigid body interaction problem with slip boundary condition

We consider a coupled PDE-ODE system describing the motion of the rigid body in a container filled with the incompressible, viscous fluid. The fluid and the rigid body are coupled via Navier slip boundary condition. We prove that the local in time strong solution is unique in the larger class of weak solutions on the interval of its existence. This is the first weak-strong uniqueness result in the area of fluid-structure interaction with a moving boundary.

math.AP↗
arXiv2017

Flow of heat conducting fluid in a time dependent domain

We consider a flow of heat conducting fluid inside a moving domain whose shape in time is prescribed. The flow in this case is governed by the Navier-Stokes-Fourier system consisting of equation of continuity, momentum balance, entropy balance and energy equality. The velocity is supposed to fulfill the full-slip boundary condition and we assume that the fluid is thermally isolated. In the presented article we show the existence of a variational solution.

math.AP↗
arXiv2017

Global existence of a radiative Euler system coupled to an electromagnetic field

We study the Cauchy problem for a system of equations corresponding to a singular limit of radiative hydrodynamics, namely the 3D radiative compressible Euler system coupled to an electromagnetic field. Assuming smallness hypotheses for the data, we prove that the problem admits a unique global smooth solution and study its asymptotics.

math.AP↗
arXiv2017

Derivation of the Navier - Stokes - Poisson system with radiation for an accretion disk

We study the 3-D compressible barotropic radiation fluid dynamics system describing the motion of the compressible rotating viscous fluid with gravitation and radiation confined to a straight layer. We show that weak solutions in the 3-D domain converge to the strong solution of the rotating 2-D Navier-Stokes-Poisson system with radiation for all times less than the maximal life time of the strong solution of the 2-D system when the Froude number is small or to the strong solution of the rotating pure 2-D Navier- Stokes system with radiation.

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arXiv2016

The rotating Navier- Stokes- Fourier- Poisson system on thin domains

We consider the compressible Navier - Stokes - Fourier - Poisson system describing the motion of a viscous heat conducting rotating fluid confined to a straight layer $ Ω_ε = ω\times (0,ε) $, where $ω$ is a 2-D domain. The aim of this paper is to show that the weak solutions in the 3D domain converge to the strong solution of the 2-D Navier - Stokes - Fourier - Poisson system $ω$ as $ε\to 0$ on the time interval, where the strong solution exists. We consider two different regimes in dependence on the asymptotic behaviour of the Froude number.

math.AP↗
arXiv2015

Weak solutions to the full Navier-Stokes-Fourier system with slip boundary conditions in time dependent domains

We consider the compressible Navier-Stokes-Fourier system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. Assuming that the pressure can be decomposed into an elastic part and a thermal part, we prove global-in-time existence of weak solutions. Our approach is based on the penalization of the boundary behavior, viscosity, and the pressure in the weak formulation. Moreover, the thermal energy equation is in the weak formulation replaced by the thermal energy inequality complemented with the global total energy inequality. In the approximation scheme the thermal energy inequality is consider to be satisfied in the renormalized sense.

math.AP↗
arXiv2015

Asymptotic structure of viscous incompressible flow around a rotating body, with nonvanishing flow field at infinity

We consider weak (''Leray'') solutions to the stationary Navier-Stokes system with Oseen and rotational terms, in an exterior domain. It is shown the velocity may be split into a constant times the first column of the fundamental solution of the Oseen system, plus a remainder term decaying pointwise near infinity at a rate which is higher than the decay rate of the Oseen tensor. This result improves the theory by M. Kyed, Asymptotic profile of a linearized flow past a rotating body, Q. Appl. Math. 71 (2013), 489-500.

math.AP↗
arXiv2015

Leading terms of velocity and its gradient of the stationary rotational viscous incompressible flows with nonzero velocity at infinity

We consider the Navier-Stokes system with Oseen and rotational terms describing the stationary flow of a viscous incompressible fluid around a rigid body moving at a constant velocity and rotating at a constant angular velocity. In a previous paper, we prove a representation formula for weak solutions of the system. Here the representation formula is used to get an asymptotic expansion of respectively velocity and its gradient, and to establish pointwise decay estimates of remainder terms. Our results are based on a fundamental solution proposed by Guenther and Thomann J. Math. Fluid Mech., 8 (2006), 77-98. We thus present a different approach to this result, besides the one, given by Kyed J. Math. Soc. Japan, 66 (2014), 1-16.

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