In this paper we show that every diffusive system is a well-posed system in the sense of Salamon and Weiss. Furthermore, we characterize several systems theoretic properties of these systems, such as stability, controllability, and observability. Instead of referring to general results on well-posed linear system, we prove these results directly. Hence we hope that this paper will serve as a tu...

We deal with well-posedness and asymptotic dynamics of a class of coupled systems consisting of linearized 3D Navier–Stokes equations in a bounded domain and a classical (nonlinear) elastic plate/shell equation. We consider three models for plate/shell oscillations: (a) the model which accounts for transversal displacement of a flexible flat part of the boundary only, (b) the model for in-plane...

We study the asymptotic expansion of solutions to the linearized compressible Navier-Stokes equations with highly oscillatory forces in the half-plane with nonslip boundary conditions for small viscosity. The wave length of oscillations is assumed to be proportional to the square root of the viscosity. By means of asymptotic analysis, we deduce that the zero-viscosity limit of solutions satisfi...

Theorems on the Fredholm alternative and well-posedness of the linear boundary value problem u′(t)= (u)(t) + q(t), h(u)= c, where : C([a,b];R)→ L([a,b];R) and h : C([a, b];R)→ R are linear bounded operators, q ∈ L([a,b];R), and c ∈ R, are established even in the case when is not a strongly bounded operator. The question on the dimension of the solution space of the homogeneous equation u′(t)= (...

This paper is dedicated to the study of the initial value problem for density dependent incompressible viscous fluids in R with N ≥ 2. We address the question of well-posedness for large data having critical Besov regularity and we aim at stating well-posedness in functional spaces as close as possible to the ones imposed in the incompressible Navier Stokes system by Cannone, Meyer and Planchon...

In this paper we consider the following 2D Boussinesq-Navier-Stokes systems ∂tu+ u · ∇u+∇p+ |D|u = θe2 ∂tθ + u · ∇θ + |D|θ = 0 with divu = 0 and 0 < β < α < 1. When 6− √ 6 4 < α < 1, 1−α < β ≤ f(α), where f(α) is an explicit function as a technical bound, we prove global well-posedness results for rough initial data. Mathematics Subject Classification (2000): 76D03, 76D05, 35B33, 35Q35

i=2 ξi(x, t)vi−1(t){(Ai(zi−1(t)− zi(t))) − ‖zi−1(t)− zi(t)‖ 2 R3 ‖zi+1(t)− zi(t)‖R3 (Bi(zi+1(t)− zi(t)))}. (3) In the above, Ω is a bounded domain in R with boundary ∂Ω of class C, y(x, t) and p(x, t) are respectively the velocity and the pressure of the fluid at point x = (x1, x2, x3) ∈ Ω at time t, while ν is the kinematic viscosity constant. The swimmer in (1)–(3) is modeled as a collection ...