Lucas C. F. Ferreira

The asymptotic behaviour of subcritical dissipative quasi-geostrophic equations

In this work, we give a complete description of the asymptotic behaviour of quasi-geostrophic equations in the subcritical range . We first show that its solutions simplify asymptotically as t → ∞. More precisely, solutions behave as a particular self-similar solution normalized by the mass as t → ∞ and when the initial data belong to . On the other hand, we show that solutions with initial data in decay towards zero as t → ∞ in this space. All results are obtained regardless of the size of the initial condition.

Well-posedness and asymptotic behaviour for the convection problem in

We analyse the well-posedness of the initial value problem for a convection problem. Mild solutions are obtained in the weak- spaces and the existence of self-similar solutions is shown, while the only small self-similar solution in the Lebesgue space is the null solution. The asymptotic stability of solutions is analysed and, as a consequence, a criterion of self-similarity persistence at large times is obtained.

Blinded-key signatures: securing private keys embedded in mobile agents

We present a new cryptographic primitive, the blinded-key signature, which allows the inclusion of private keys in autonomous mobile agents. This novel approach can be applied to many well-known digital signature schemes, such as RSA and ElGammal.

Existence and asymptotic behaviour for the parabolic-parabolic Keller-Segel system with singular data

This work considers the Keller–Segel system of parabolic–parabolic type in for n ≥ 2. We prove existence results in a new framework and with initial data in . This initial data class is larger than the previous ones, e.g., Kozono–Sugiyama (2008 Indiana Univ. Math. J. 57 1467–500) and Biler (1998 Adv. Math. Sci. Appl. 8 715–43), and covers physical cases of initial aggregation at points (Diracs) and on filaments. Self-similar solutions are obtained for initial data with the correct homogeneity and a certain value of parameter γ. We also show an asymptotic behaviour result, which provides a basin of attraction around each self-similar solution.

On the Nonhomogeneous Navier--Stokes System with Navier Friction Boundary Conditions

We address the issue of existence of weak solutions for the nonhomogeneous Navier--Stokes system with Navier friction boundary conditions allowing the presence of vacuum zones and assuming rough conditions on the data. We also study the convergence, as the viscosity goes to zero, of weak solutions for the nonhomogeneous Navier--Stokes system with Navier friction boundary conditions to the strong solution of the Euler equations with variable density, provided that the initial data converge in

Existence of solutions to the convection problem in a pseudomeasure-type space

L^{2}

On the existence of infinite energy solutions for nonlinear Schrödinger equations

to a smooth enough limit.

Gradient flows of time-dependent functionals in metric spaces and applications to PDEs

We study the well-posedness of a convection problem in a pseudomeasure-type space PMa, without assuming that the gravitational field is bounded. Considering the PMa space with right homogeneity, the existence of self-similar solutions is proved. Finally, an analysis about asymptotic stability is made.

A family of dissipative active scalar equations with singular velocity and measure initial data

r. We derive new results about existence and uniqueness of local and global solutions for the nonlinear Schrodinger equation, including self-similar solutions. Our analysis is performed in the framework of weak-L P spaces.

Global well-posedness and symmetries for dissipative active scalar equations with positive-order couplings

We develop a gradient-flow theory for time-dependent functionals defined in abstract metric spaces. Global well-posedness and asymptotic behavior of solutions are provided. Conditions on functionals and metric spaces allow to consider the Wasserstein space