Revista Matemática Iberoamericana


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Volume 34, Issue 1, 2018, pp. 355–395
DOI: 10.4171/RMI/988

Published online: 2018-02-06

Global well-posedness of 3-D inhomogeneous Navier–Stokes system with ill-prepared initial data

Ping Zhang[1] and Zhifei Zhang[2]

(1) Chinese Academy of Sciences, Beijing, China
(2) Peking University, Beijing, China

In this paper, we investigate the global well-posedness of 3-D incompressible inhomogeneous Navier–Stokes system with ill-prepared initial data of the form $$\bigl(1+\epsilon^{\beta}a_0(x_{\rm h},\epsilon x_3),(\epsilon^{1-\alpha}\,v^{\rm h}_0, \epsilon^{-\alpha}v_0^3)(x_{\rm h},\epsilon x_3)\bigr)$$ for any $\alpha \in ]0,1/3[, \beta > 2\alpha$, and $\epsilon$ being sufficiently small. This result improves the global well-posedness result for so-called well-prepared initial data, which corresponds to the case of $\alpha=0$.

Keywords: Inhomogeneous Navier–Stokes system, well-posedness

Zhang Ping, Zhang Zhifei: Global well-posedness of 3-D inhomogeneous Navier–Stokes system with ill-prepared initial data. Rev. Mat. Iberoamericana 34 (2018), 355-395. doi: 10.4171/RMI/988