arXiv subjects

Riccardo Voso

Publications and source records attributed to Riccardo Voso.

3 recordsLinked to original sources

arXiv2024

Analysis of a Navier-Stokes phase-field crystal system

We consider an evolution system modeling a flow of colloidal particles which are suspended in an incompressible fluid and accounts for colloidal crystallization. The system consists of the Navier-Stokes equations for the volume averaged velocity coupled with the so-called Phase-Field Crystal equation for the density deviation. Considering this system in a periodic domain and assuming that the viscosity as well as the mobility depend on the density deviation, we first prove the existence of a weak solution in dimension three. Then, in dimension two, we establish the existence of a (unique) strong solution.

math.AP↗

arXiv2024

Weighted Energy-Dissipation approach to semilinear gradient flows with state-dependent dissipation

We investigate the Weighted Energy-Dissipation variational approach to semilinear gradient flows with state-dependent dissipation. A family of parameter-dependent functionals defined over entire trajectories is introduced and proved to admit global minimizers. These global minimizers correspond to solutions of elliptic-in-time regularizations of the limiting causal problem. By passing to the limit in the parameter we prove that such global minimizers converge, up to subsequences, to a solution of the gradient flow.

math.AP↗

arXiv2024

Optimal control of gradient flows via the Weighted Energy-Dissipation method

We consider a general optimal control problem in the setting of gradient flows. Two approximations of the problem are presented, both relying on the variational reformulation of gradient-flow dynamics via the Weighted-Energy-Dissipation variational approach. This consists in the minimization of global-in-time functionals over trajectories, combined with a limit passage. We show that the original nonpenalized problem and the two successive approximations admits solutions. Moreover, resorting to a $Γ$-convergence analysis we show that penalised optimal controls converge to nonpenalized one as the approximation is removed.

math.OC↗