Related papers: Determining Projections and Functionals for Weak S…
We prove a weak stability result for the three-dimensional homogeneous incompressible Navier-Stokes system. More precisely, we investigate the following problem : if a sequence $(u_{0, n})_{n\in \N}$ of initial data, bounded in some scaling…
We construct global weak solutions to isothermal quantum Navier-Stokes equations, with or without Korteweg term, in the whole space of dimension at most three. Instead of working on the initial set of unknown functions, we consider an…
This is an expository paper on the theory of local regularity for weak solutions to the non-stationary 3D Navier-Stokes equations near the boundary of a domain.
We prove the global existence of weak solutions of the one-dimensional Navier-Stokes-Korteweg (NSK) equations when the viscosity and the capillarity coefficients are power functions of the density, which may be zero on a set with positive…
This paper investigates boundary hemivariational inequality problems associated with both stationary and non-stationary two and three-dimensional convective Brinkman-Forchheimer equations (or Navier-stokes equations with damping), which…
We show that the eigenvalues of the Stokes operator in a domain with a small hole converge to the eigenvalues of the Stokes operator in the whole domain, when the diameter of the hole tends to 0. The convergence of the eigenspaces and the…
The existence of suitable weak solutions of 3D Navier-Stokes equations, driven by a random body force, is proved. These solutions satisfy a local balance of energy. Moreover it is proved also the existence of a statistically stationary…
The continuity of the kinetic energy is an important property of incompressible viscous fluid flows. We show that for any prescribed finite energy divergence-free initial data there exist infinitely many global in time weak solutions with…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
In this paper, we study the connectedness and compactness of the attainability set of weak solutions to the three-dimensional Navier--Stokes equations with damping. Depending on the value of the parameter \b{eta}, which controls the damping…
In this paper, we address two main topics. First, we study the problem of minimizing the sum of a smooth function and the composition of a weakly convex function with a linear operator on a closed vector subspace. For this problem, we…
We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime $L^2$ weak limit of Leray--Hopf weak solutions of the Navier-Stokes equations on any…
We prove a uniqueness result for weak solutions to the Vlasov-Navier-Stokes system in two dimensions, both in the whole space and in the periodic case, under a mild decay condition on the initial distribution function. The main result is…
We consider the Navier-Stokes equations with Navier's slip boundary conditions in a three-dimensional curved thin domain around a given closed surface. Under suitable assumptions we show that the average in the thin direction of a strong…
We consider the Navier-Stokes equations on thin 3D domains, supplemented mainly with purely periodic boundary conditions or with periodic boundary conditions in the thin direction and homogeneous Dirichlet conditions on the lateral…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
Inspired by some experimental (numerical) works on fractional diffusion PDEs, we develop a rigorous framework to prove that solutions to the fractional Navier-Stokes equations, which involve the fractional Laplacian operator…
We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem…
We study the non-uniqueness of weak solutions for the two-dimensional hyper-dissipative Navier-Stokes equations in the super-critical spaces $L_{t}^{\gamma}L_{x}^{p}$ when $\alpha\in[1,\frac{3}{2})$, and obtain the conclusion that the…
We deal with a weak solution v to the Navier-Stokes initial value problem in R^3 x(0,T). We denote by \omega^+ a spectral projection of \omega=\curl\, v, defined by means of the spectral resolution of identity associated with the…