Solutions to three-dimensional Navier-Stokes equations for incompressible fluids.
Solvability of a three-dimensional boundary value problem with a free surface for the stationary Navier-Stokes system
Solvability of evolution problems for viscious incompressible flow in domains with non-compact boundaries
Solvability of the Navier-Stokes equations on manifolds with boundary.
Solvability of two stationary free boundary problems for the Navier-Stokes equations
Si studiano due problemi con frontiera libera per equazioni stazionarie di Navier-Stokes: il problema del movimento di un liquido viscoso incomprimibile generato dalla rotazione di una sbarra rigida immersa nel liquido con velocità angolare assegnata e il problema della fuoriuscita di un liquido da un tubo circolare nello spazio libero. Si assegna l'angolo di contatto tra la frontiera libera e la superficie del tubo e, nel secondo problema, il flusso totale del liquido attraverso l'apertura del...
Some application of the implicit function theorem to the stationary Navier-Stokes equations
We prove that - in the case of typical external forces - the set of stationary solutions of the Navier-Stokes equations is the limit of the (full) sequence of sets of solutions of the appropriate Galerkin equations, in the sense of the Hausdorff metric (for every inner approximation of the space of velocities). Then the uniqueness of the N-S equations is equivalent to the uniqueness of almost every of these Galerkin equations.
Some globally stable approximations for the Navier-Stokes equations and for some other equations of viscous incompressible fluids
Some inverse and control problems for fluids
This paper deals with some inverse and control problems for the Navier-Stokes and related systems. We will focus on some particular aspects that have recently led to interesting (theoretical and numerical) results: geometric inverse problems, Eulerian and Lagrangian controllability and vortex reduction oriented to shape optimization.
Some new existence results for the variable density Navier-Stokes equations
Some new regularity criteria for the Navier-Stokes equations containing gradient of the velocity
We study the nonstationary Navier-Stokes equations in the entire three-dimensional space and give some criteria on certain components of gradient of the velocity which ensure its global-in-time smoothness.
Some notes to the transport equation and to the Green formula
Some orthogonal decompositions of Sobolev spaces and applications
Two kinds of orthogonal decompositions of the Sobolev space W̊₂¹ and hence also of for bounded domains are given. They originate from a decomposition of W̊₂¹ into the orthogonal sum of the subspace of the -solenoidal functions, k ≥ 1, and its explicitly given orthogonal complement. This decomposition is developed in the real as well as in the complex case. For the solenoidal subspace (k = 0) the decomposition appears in a little different form. In the second kind decomposition the -solenoidal...
Some problems of vector analysis in solenoidal spaces
Some recent results on the existence of global-in-time weak solutions to the Navier-Stokes equations of a general barotropic fluid
Some recent results on the existence of global-in-time weak solutions to the Navier-Stokes equations of a general barotropic fluid
This is a survey of some recent results on the existence of globally defined weak solutions to the Navier-Stokes equations of a viscous compressible fluid with a general barotropic pressure-density relation.
Some recent results on the Muskat problem
We consider the dynamics of an interface given by two incompressible fluids with different characteristics evolving by Darcy’s law. This scenario is known as the Muskat problem, being in 2D mathematically analogous to the two-phase Hele-Shaw cell. The purpose of this paper is to outline recent results on local existence, weak solutions, maximum principles and global existence.
Some remarks on Prandtl system
The purpose of this paper is to correct some drawbacks in the proof of the well-known Boundary Layer Theory in Oleinik’s book. The Prandtl system for a nonstationary layer arising in an axially symmetric incopressible flow past a solid body is analyzed.
Some remarks on the Navier-Stokes equations with regularity in one direction
We review the developments of the regularity criteria for the Navier-Stokes equations, and make some further improvements.
Some remarks on the non-uniqueness of the stationary solutions of Navier-Stokes equations.
Some remarks to the compactness of steady compressible isentropic Navier-Stokes equations via the decomposition method
In [18]–[19], P.L. Lions studied (among others) the compactness and regularity of weak solutions to steady compressible Navier-Stokes equations in the isentropic regime with arbitrary large external data, in particular, in bounded domains. Here we investigate the same problem, combining his ideas with the method of decomposition proposed by Padula and myself in [29]. We find the compactness of the incompressible part of the velocity field and we give a new proof of the compactness of the “effective...