Matteo Caggio

Matteo Caggio
Institute of Mathematics of the Czech Academy of Sciences · Evolution Differential Equations (EDE)

MD Physics, PhD Mathematics

About

25
Publications
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56
Citations

Publications

Publications (25)
Article
In this paper we study the incompressible inviscid limit for a compressible micro-polar model. We prove that the weak solution of the compressible micro-polar system converges to the solution of the Navier–Stokes equations (Euler equations) in the limit of small Mach number (and vanishing viscosity).
Conference Paper
This paper presents rst few results obtained using a newly developed test code aimed at validation and cross-comparison of turbulence models to be applied in environmental flows. A simple code based on nite di erence discretization is constructed to solve steady flows of incompresible non-homogeneous (variable denstity) fluids. For the rst tests a...
Article
Full-text available
We consider a coupled system of partial and ordinary differential equations describing the interaction between an incompressible inviscid fluid and a rigid body moving freely inside the fluid. We prove the existence of measure-valued solutions which is generated by the vanishing viscosity limit of incompressible fluid–rigid body interaction system...
Preprint
In this paper we study the incompressible inviscid limit for a compressible micro-polar model. We prove that the weak solution of the compressible micro-polar system converges to the solution of the Navier-Stokes equations (Euler equations) in the limit of small Mach number (and vanishing viscosity).
Article
The aim of this paper is to investigate the regime of high Mach number flows for compressible barotropic fluids of Korteweg type with density dependent viscosity. In particular we consider the models for isothermal capillary and quantum compressible fluids. For the capillary case we prove the existence of weak solutions and related properties for t...
Article
Full-text available
We investigate the upper bound on the vertical heat transport in the fully 3D Rayleigh–Bénard convection problem at the infinite Prandtl number for a micropolar fluid. We obtain a bound, given by the cube root of the Rayleigh number, with a logarithmic correction. The derived bound is compared with the optimal known one for the Newtonian fluid. It...
Article
We consider the compressible Euler system describing the motion of an ideal fluid confined to a straight layer \(\Omega _{\delta }=(0,\delta )\times {\mathbb {R}}^2, \ \ \delta >0\). In the framework of dissipative measure-valued solutions, we show the convergence to the strong solution of the 2D incompressible Euler system when the Mach number ten...
Preprint
Full-text available
We consider a compressible Navier-Stokes system for a barotropic fluid with density dependent viscosity in a three-dimensional time-space domain $(0,T)\times \Omega_\varepsilon$ where $\Omega_\varepsilon = (0,\varepsilon)^2\times (0,1)$. We show that the weak solutions of the 3D system converges to the strong solution of the respective 1D system as...
Preprint
Full-text available
We consider a coupled system of partial and ordinary differential equations describing the interaction between an isentropic inviscid fluid and a rigid body moving freely inside the fluid. We prove the existence of measure-valued solutions which is generated by the vanishing viscosity limit of incompressible fluid-rigid body interaction system unde...
Preprint
The aim of this paper is to investigate the regime of high Mach number flows for compressible barotropic fluids of Korteweg type with density dependent viscosity. In particular we consider the models for isothermal capillary and quantum compressible fluids. For the capillary case we prove the existence of weak solutions and related properties for t...
Preprint
We consider the compressible Euler system describing the motion of an ideal fluid confined to a straight layer $\Omega_{\delta}=(0,\delta)\times\mathbb{R}^2, \ \ \delta>0$. In the framework of dissipative measure-valued solutions, we show the convergence to the strong solution of the 2D incompressible Euler system when the Mach number tends to zero...
Preprint
We consider the compressible Navier-Stokes system describing the motion of a viscous fluid confined to a straight layer $\Omega_{\delta}=(0,\delta)\times\mathbb{R}^2$. 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 $\epsilon $...
Article
We consider the inviscid incompressible limits of the rotating compressible Navier–Stokes system for a barotropic fluid. We show that the limit system is represented by the rotating incompressible Euler equation on the whole space.
Article
We study the regularity criteria for the incompressible Navier–Stokes equations in the whole space based on one velocity component, namely , and . We use a generalization of the Troisi inequality and anisotropic Lebesgue spaces and prove, for example, that the condition , where and , yields the regularity of on .
Article
Full-text available
We consider the compressible Navier - Stokes - Fourier - Poisson system describing the motion of a viscous heat conducting rotating fluid confined to a straight layer $ \Omega_{\epsilon} = \omega \times (0,\epsilon) $, where $\omega$ 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 so...