Paolo Antonelli, Michele Dolce, Pierangelo Marcati
AbstractIn this paper, we study the linear stability properties of perturbations
around the homogeneous Couette flow for a 2D isentropic compressible fluid in
the domain$$\mathbb {T}\times \mathbb {R}$$T×R. In the inviscid case there is a
generic Lyapunov type instability for the density and the irrotational component
of the velocity field. More precisely, we prove that their$$L^2$$L2norm grows
as... hiện toàn bộ
AbstractWe consider a sequence of approximate solutions to the compressible
Euler system admitting uniform energy bounds and/or satisfying the relevant
field equations modulo an error vanishing in the asymptotic limit. We show that
such a sequence either (i) converges strongly in the energy norm, or (ii) the
limit is not a weak solution of the associated Euler system. This is in sharp
contrast to ... hiện toàn bộ