论文标题
长期规律性的二维Navier-Stokes-Poisson方程
Long-term regularity of two dimensional Navier-Stokes-Poisson equations
论文作者
论文摘要
该手稿致力于2-D Navier-Stokes-Poisson系统的长期规律性。我们允许初始密度接近常数，并且初始速度的潜在部分与重新固定的粘度参数$ \ varepsilon $独立于小，而与$ \ varepsilon $相比，初始速度的旋转部分被认为很小。然后，我们证明系统的寿命$ t^{\ varepsilon} $满足$ t^{\ varepsilon}> \ varepsilon^{ - （1- \ vartheta）} $，其中小常数$ \ vartheta $是在某些合适的空间中的初始扰动大小。正常形式的转化和经典的抛物线能量估计是证明的主要成分。
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 $\varepsilon$ while the rotational part of the initial velocity is assumed to be small compared to $\varepsilon$. We then show that the lifespan of the system $T^{\varepsilon}$ satisfies $T^{\varepsilon}>\varepsilon^{-(1-\vartheta)}$, 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.
