Strong periodic solutions for a class of abstract evolution equations

Periodic solutions in unbounded domains for the Boussinesq system

“…To avoid some technical complexities in the study of (1.1)-(1.5), throughout this paper we assume Ψ = 0. Several works have been made in the mathematical analysis of system (1.1)-(1.5); see, for instance, [3], [5], [7], [13], [6] and papers cited therein. The time-periodic solutions for the Boussinesq equations in bounded domains was considered in [13].…”

“…The analysis was made via the Galerkin's method. Indeed, in [13] it was considered a class of nonlinear evolution equations in a separable Hilbert space generalizing several models of hydrodynamics. However, the study of periodic solutions for system (1.1)-(1.…”

Reproductivity for a nematic liquid crystal model

“…d = 0), it is known an argument that provides (global in time) regularity of any reproductive solution associated to regular and small enough data [6]. In [11] this argument is applied to an abstract parabolic problem, which is a generalization of some of the main hydrodynamic models.…”

Existence and uniqueness of strong solution for the incompressible micropolar fluid equations in domains of $${\mathbb{R}^3}$$

“…By using and interactive approach Rojas-Medar and Ortega-Torres [23] show the existence and uniqueness of the strong solutions in bounded domains in the L 2 -context. The existence and uniqueness of periodic strong solutions was done in [12] using the Galerkin method. Yamaguchi [29] also studied the problem (1)- (2) in bounded domains using the semigroup approach in L p , 1 < p < ∞; he shows the existence of global strong solutions for small data.…”