3 research outputs found
Some Controllability Results for Linearized Compressible Navier-Stokes System
In this article, we study the null controllability of linearized compressible
Navier-Stokes system in one and two dimension. We first study the
one-dimensional compressible Navier-Stokes system for non-barotropic fluid
linearized around a constant steady state. We prove that the linearized system
around , with is
not null controllable by localized interior control or by boundary control. But
the system is null controllable by interior controls acting everywhere in the
velocity and temperature equation for regular initial condition. We also prove
that the the one-dimensional compressible Navier-Stokes system for
non-barotropic fluid linearized around a constant steady state , with is not
null controllable by localized interior control or by boundary control for
small time Next we consider two-dimensional compressible Navier-Stokes
system for barotropic fluid linearized around a constant steady state We prove that this system is also not null controllable by
localized interior control
Some controllability results for linear viscoelastic fluids
We analyze the controllability properties of systems which provide a description, at first approximation, of a kind of viscoelastic fluid. We consider linear Maxwell fluids. First, we establish the large time approximate-finite dimensional controllability of the system, with distributed or boundary controls supported by arbitrary small sets. Then, we prove the large time exact controllability of fluids of the same kind with controls supported by suitable large sets. The proofs of these results rely on classical arguments. In particular, the approximate controllability result is implied by appropriate unique continuation properties, while exact controllability is a consequence
of observability (inverse) inequalities. We also discuss questions concerning the controllability of viscoelastic fluids and some related open problems.Ministerio de Ciencia e Innovació