Communications in Mathematical Sciences
Volume 18 (2020)
The unique global solvability of multi-dimensional compressible Navier–Stokes–Poisson–Korteweg model
Pages: 2169 – 2190
The present paper is dedicated to the study of the Cauchy problem for compressible Navier–Stokes–Poisson–Korteweg model in any dimension $d \geq 2$, which simultaneously involves the lower order potential term and the higher order capillarity term. The unique global solvability of the system is obtained when the initial data are close to a stable equilibrium state in a functional setting invariant by the scaling of the associated equations. In particular, one may construct the unique global solution for a class of large highly oscillating initial velocities in physical dimensions $d=2,3$.
unique global solvability, highly oscillating velocity, compressible Navier–Stokes–Poisson–Korteweg model, critical Besov spaces
2010 Mathematics Subject Classification
Fuyi Xu is partially supported by the National Natural Science Foundation of China (11501332,11771043,51976112), the Natural Science Foundation of Shandong Province (ZR2015AL007), and Young Scholars Research Fund of Shandong University of Technology. Yeping Li is partially supported by the National Natural Science Foundation of China (11671134).
Received 7 October 2019
Accepted 7 June 2020
Published 22 December 2020