Related papers: Statistical conservation laws for scalar model pro…
In this paper, we study the Navier-Stokes-Korteweg equations governed by the evolution of compressible fluids with capillarity effects. We first investigate the global well-posedness of solution in the critical Besov space for large initial…
An open problem arising in the statistical description of turbulence is related to the \textit{theoretical prediction based on first principles} of the so-called multi-point velocity probability density functions (PDFs) characterizing a…
In this paper, we prove some results on the existence and decay properties of high order derivatives in time and space variables for local and global solutions of the Cauchy problem for the Navier-Stokes equations in Bessel-potential…
New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are…
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…
Exponential stabilizability of the incompressible Navier-Stokes equations under dynamic slip boundary conditions toward arbitrary time-dependent trajectories is proven. The feedback control law is constructed explicitly using oblique…
We develop a high-fidelity numerical solver for the compressible Navier-Stokes equations, with the main aim of highlighting the predictive capabilities of low-diffusive numerics for flows in complex geometries. The space discretization of…
Loosely speaking, the Navier-Stokes-$\alpha$ model and the Navier-Stokes equations differ by a spatial filtration parametrized by a scale denoted $\alpha$. Starting from a strong two-dimensional solution to the Navier-Stokes-$\alpha$ model…
Here we investigate the Cauchy problem for the inhomogeneous Navier-Stokes equations in the whole $n$-dimensional space. Under some smallness assumption on the data, we show the existence of global-in-time unique solutions in a critical…
We consider local balances of momentum and angular momentum for the incompressible Navier-Stokes equations. First, we formulate new weak forms of the physical balances (conservation laws) of these quantities, and prove they are equivalent…
In this paper we consider a conservative discretization of the two-dimensional incompressible Navier--Stokes equations. We propose an extension of Arakawa's classical finite difference scheme for fluid flow in the vorticity-stream function…
In our previous paper [12] (Rev. Math. Phys. 16, 383-420 (2004)), a general framework was outlined to treat the approximate solutions of semilinear evolution equations; more precisely, a scheme was presented to infer from an approximate…
Hydrodynamics can be formulated as the gradient expansion of conserved currents in terms of the fundamental fields describing the near-equilibrium fluid flow. In the relativistic case, the Navier-Stokes equations follow from the…
In this paper we establish local and global existence and uniqueness of solutions for general nonlinear evolution equations with coefficients satisfying some local monotonicity and generalized coercivity conditions. An analogous result is…
We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an…
In this paper, we investigate the convergence of solutions of a stochastic representation of the three-dimensional Navier-Stokes equations to those of their primitive equations counterpart. Our analysis covers both weak and strong…
The system of equations of one-dimensional shallow water over uneven bottom in Euler's and Lagrange's variables is considered. Intermediate system of equations is introduced. Hydrodynamic conservation laws of intermediate system of…
In this paper, we present a new computational framework to approximate a Cahn-Hilliard-Navier-Stokes model with variable density and degenerate mobility that preserves the mass of the mixture, the pointwise bounds of the density and the…
We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general…
We present a numerical scheme for approximating the incompressible Navier-Stokes equations based on an auxiliary variable associated with the total system energy. By introducing a dynamic equation for the auxiliary variable and…