Long-term regularity of two dimensional Navier-Stokes-Poisson equations

Abstract

This manuscript is devoted to the long-term regularity of the 2-d Navier-Stokes-Poisson system. We allow the initial density to be close to a constant and the potential part of the initial velocity to be small independently of the rescaled viscosity parameter $\epsilon$ while the rotational part of the initial velocity is assumed to be small compared to $\epsilon$. We then show that the lifespan of the system $T^{\epsilon }$ satisfies $T^{\epsilon }>{\epsilon }^{-(1-\vartheta )}$, where the small constant $\vartheta$ is the size of the initial perturbation in some suitable space. The normal form transformation and the classical parabolic energy estimates are the main ingredients of the proof.

arXiv comment43 pages, any comments are welcome

References in corpus (4)

• Global Smooth Ion Dynamics in the Euler-Poisson System
• Global existence for compressible Navier-Stokes-Poisson equations in three and higher dimensions
• The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings
• Large time existence of Euler-Korteweg equations and two-fluid Euler-Maxwell equations with vorticity