Global existence and exponential stability of solutions in \(H^4\) for the compressible Navier-Stokes equations with the cylinder symmetry (Q994297)

The non steady, compressible axisymmetric Navier-Stokes equations are considered. It is supposed that the functions depend only on the radial variable. Assuming that the initial total energy is small enough, the authors prove that there exists a unique global solution in \(H^4\) for the considered problem. Moreover, the exponential stability of the solution in \(H^4\) is established. The previous properties obtained in \(H^4\) imply the same properties for classical solutions.