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Finite energy Navier-Stokes flows with unbounded gradients induced by localized flux in the half-space
时间:2022年12月21日 12:31 点击数:


报告地点:腾讯会议ID:582 821 105




For the Stokes system in the half space, Kang [Math.~Ann.~2005] showed that a solution generated by a compactly supported, H\"older continuous boundary flux may have unbounded normal derivatives near the boundary. In this paper we first prove explicit global pointwise estimates of the above solution, showing in particular that it has finite global energy and its derivatives blow up everywhere on the boundary away from the flux. We then use the above solution as a profile to construct solutions of the Navier-Stokes equations which also have finite global energy and unbounded normal derivatives due to the flux. Our main tool is the pointwise estimates of the Green tensor of the Stokes system proved by us. We also examine the Stokes flows generated by dipole bumps boundary flux, and identify the regions where the normal derivatives of the solutions tend to positive or negative infinity near the boundary. This is a joint work with Kyungkeun Kang, Chen-Chih Lai and Tai-Peng Tsai.


湖南师范大学Bwin国际教授,博士生导师。主要关注流体力学方程的数学理论研究。相关论文发表在Adv. Math, TAMS, SIMA, JDE等著名数学期刊,主持多项国家自然科学基金项目。

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