Stationary solutions to outflow problem for 1-D compressible fluid models of Korteweg type: Existence, stability and convergence rate

Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Hakho HongAbstractIn this paper, we are concerned with the outflow problem in the half line (0,∞) to the isothermal compressible Navier–Stokes–Korteweg system with a nonlinear boundary condition for vanishing capillary tensor at x=0. We first give some necessary and sufficient conditions for the existence of the stationary solutions with the aid of center manifold theory. We also show the stability of the stationary solutions under smallness assumptions on the initial perturbation in the Sobolev space, by employing an energy method. Moreover, the convergence rate of the solution toward the stationary solutions is obtained, provided that the initial perturbations belong to the weighted Sobolev spaces.

Source: Nonlinear Analysis: Real World Applications - November 20, 2019 Category: Research Source Type: research