Global well-posedness for the two-dimensional nonlinear Boussinesq equations with vertical dissipation

作者：Wu Gang^*; Zheng Xiaoxin

来源：Journal of Differential Equations, 2013, 255(9): 2891-2926.

DOI：10.1016/j.jde.2013.07.023

• Nonlinear Boussinesq equations
• Growth estimate
• Vertical dissipation
• Global well-posedness

The present paper is devoted to the study of the global well-posedness for the two-dimensional nonlinear Boussinesq equations with vertical dissipation. In the absence of horizontal dissipation, we establish a growth estimate on vertical component of velocity, that is, sup(p >= 2) parallel to u(2)(t)parallel to(LP)/root p log p which is close to parallel to u(2) (t)parallel to(L)infinity via the low-high decomposition technique. This together with the smoothing effect in vertical direction enables us to obtain the H-1-estimate for velocity. Based on this, we prove the existence and uniqueness of classical solution without smallness assumptions. In addition, we also discuss the global well-posedness result for the rough initial data.

• 出版日期2013-11-1
• 单位中国工程物理研究院; 中国科学院大学