Related papers: Generalized Eulerian-Lagrangian description of Nav…
Fluid configurations in three-dimensions, displaying a plausible decay of regularity in a finite time, are suitably built and examined. Vortex rings are the primary ingredients in this study. The full Navier-Stokes system is converted into…
We investigate the effect of a four-dimensional Fourier transform on the formulation of the Navier-Stokes equation in Fourier space and the way the energy is transferred between Fourier components. Since time in a sampled high intensity…
This paper studies the two-dimensional inhomogeneous Navier--Stokes equations governing stratified flows in a bounded domain under a gravitational potential \(f\). Our main results are as follows. First, we provide a rigorous…
We study the Navier-Stokes and Euler equations of incompressible hydrodynamics in two and three spatial dimensions and show how the constraint of incompressiblility leads to equations of Monge--Amp\`ere type for the stream function, when…
We study a coupled Fokker-Planck--Navier-Stokes (FPNS) system modeling the dynamics of interacting particles suspended in a viscous incompressible fluid, where the coupling occurs through a locally averaged Brinkman drag force. Our main…
We are concerned with the barotropic compressible Navier-Stokes equations on the real line. Our primary goal is to establish the global well-posedness in a critical regularity framework in the case where the initial data are small…
The collective motion of microswimmers in suspensions induce patterns of vortices on scales that are much larger than the characteristic size of a microswimmer, attaining a state called bacterial turbulence. Hydrodynamic turbulence acts on…
In this work, we investigate the Navier-Stokes equation in the presence of thermal noise, both at finite viscosity (revisiting the seminal work by Forster-Nelson-Stephen) and in the inviscid limit, which has not yet been explored. We…
We simulate numerically the full dynamics of Faraday waves in three dimensions for two incompressible and immiscible viscous fluids. The Navier-Stokes equations are solved using a finite-difference projection method coupled with a…
In the present thesis, we are interested in the description of the dynamics of flows on large scales. In this context, the fluids are governed by rotational, weak compressibility and stratification effects, whose importance is measured by…
We present a principally new method, which is not based on the Kolmogorov flows, for obtaining the lower bounds for the attractors dimensions of the equations related with hydrodynamics and apply it to the classical 2D Navier--Stokes…
Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is…
The fluid-gravity correspondence provides us with explicit spacetime metrics that are holographically dual to (non-)relativistic nonlinear hydrodynamics. The vacuum Einstein equations, in the presence of a Killing vector, possess…
Exploring the possibility of describing a fluid flow via a time-reversible equation and its relevance for the fluctuations statistics in stationary turbulent (or laminar) incompressible Navier-Stokes flows.
Ferromagnetic magnetohydrodynamics concerns the study of conducting fluids with intrinsic magnetisation under the influence of a magnetic field. It is a generalisation of the magnetohydrodynamical equations and takes into account the…
In this paper, we present a new framework for the global well-posedness and large-time behavior of a two-phase flow system, which consists of the pressureless Euler equations and incompressible Navier-Stokes equations coupled through the…
The Eulerian space-time correlation of strong Magnetohydrodynamic (MHD) turbulence in strongly magnetized plasmas is investigated by means of direct numerical simulations of Reduced MHD turbulence and phenomenological modeling. Two new…
The three-dimensional Navier-Stokes-$\alpha$ model for fast rotating geophysical fluids is considered. The Navier-Stokes-$\alpha$ model is a nonlinear dispersive regularization of the exact Navier-Stokes equations obtained by Lagrangian…
We study the global regularity, for all time and all initial data in $H^{1/2}$, of a recently introduced decimated version of the incompressible 3D Navier-Stokes (dNS) equations. The model is based on a projection of the dynamical evolution…
We consider the model of a transverse vector (e.g. magnetic) field with the most general form of the nonlinearity, known as the ${\cal A}$ model, passively advected by a strongly compressible turbulent flow, governed by the randomly stirred…