Some remarks on Weyl pseudodifferential operators
Some remarks to numerical solution of the Euler and Navier-Stokes equation
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...
Some results about blow-up and global existence to a semilinear degenerate heat equation.
Some results about dissipativity of Kolmogorov operators
Given a Hilbert space with a Borel probability measure , we prove the -dissipativity in of a Kolmogorov operator that is a perturbation, not necessarily of gradient type, of an Ornstein-Uhlenbeck operator.
Some results about multiplicity and bifurcation of stationary solutions of a reaction diffusion climatological model.
In this survey we collect several results concerning S-type bifurcation curves for the number of solutions of reaction-diffusion stationary equations. In particular, we recall several results in the literature for the case of stationary energy balance models.
Some results concerning the Poisson-Boltzmann equation
Some results in viscoelasticity theory via a simple perturbation argument
Some results of Gevrey and analytic regularity for semilinear weakly hyperbolic equations of Oleinik type
Some results of nontrivial solutions for a nonlinear PDE in Sobolev space.
Some results on critical groups for a class of functionals defined on Sobolev Banach spaces
We present critical groups estimates for a functional defined on the Banach space , bounded domain in , , associated to a quasilinear elliptic equation involving -laplacian. In spite of the lack of an Hilbert structure and of Fredholm property of the second order differential of in each critical point, we compute the critical groups of in each isolated critical point via Morse index.
Some results on eigenfunctions on symmetric spaces and eigenspace representations.
Some results on invariant measures in hydrodynamics
In questa nota, si presentano risultati di esistenza e di unicità di misure invarianti per l'equazione di Navier-Stokes che governa il moto di un fluido viscoso incomprimibile omogeneo in un dominio bidimensionale soggetto a una forzante che ha due componenti: una deterministica e una di tipo rumore bianco nella variabile temporale.
Some results on semilinear systems on the unbounded space R3.
We study in this paper some systems, using standard tools devoted to the analysis of semilinear elliptic problems on R3. These systems do not admit any non trivial radial solutions in the E1 E2 = + 1 cases. A first type of solution consists in a ground state of R (-1,-1), exhibited by variational arguments, whose structure is a finite energy perturbation of a non trivial constant solution of R (-1,-1). A second type consists in a radial, oscillating, asymptotically null at infinity solution in the...
Some results on strongly nonlinear anisotropic differential equations
The paper concerns the existence of weak solutions to nonlinear elliptic equations of the form A(u) + g(x,u,∇u) = f, where A is an operator from an appropriate anisotropic function space to its dual and the right hand side term is in with 0 < m < 1. We assume a sign condition on the nonlinear term g, but no growth restrictions on u.
Some results on the asymptotic behaviour of Hopf weak solutions to the Navier-Stokes equations in unbounded domains.
Some results on the Navier-Stokes equations in connection with the statistical theory of stationary turbulence
Some rigorous results connected with the conventional statistical theory of turbulence in both the two- and three-dimensional cases are discussed. Such results are based on the concept of stationary statistical solution, related to the notion of ensemble average for turbulence in statistical equilibrium, and concern, in particular, the mean kinetic energy and enstrophy fluxes and their corresponding cascades. Some of the results are developed here in the case of nonsmooth boundaries and a less regular...
Some results on the Pompeiu problem.
Some results on the well-posedness for systems with time dependent coefficients
We consider hyperbolic systems with time dependent coefficients and size or . We give some sufficient conditions in order the Cauchy Problem to be well-posed in and in Gevrey spaces.
Some results on the well-posedness of an integro-differential Frémond model for shape memory alloys.