The global well-posedness of one class of new initial-boundary value problem on incompressible Navier-Stokes equations and the related models in the domain with the boundary is studied. The global existence of a class of weak solution to the initial boundary value problem to two/three-dimensional incompressible Navier-Stokes equation with the pressure-velocity relation at the boundary is obtained, and the global existence and uniqueness of the smooth solution to the corresponding problem in two-dimensional case is also established. Some extends to the corresponding incompressible fluid models such as Boussinesq equation and fluid-structure interaction models etc. are given.

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王术，现为北京工业大学教授，博士生导师，北京工业大学数学一级学科博士学位授权点责任教授，北京市重点建设学科“应用数学”学科负责人，中国工业与应用数学会理事，国家留学基金委会议评审专家，国家自然科学基金会评审专家。曾任中国数学会理事、北京工业大学应用数73882必赢网页版院长等职务。主要研究：偏微分方程及其应用。现主持或曾主持国家自然科学基金8项（含重点项目1项），独立获得北京市科学技术奖二等奖1项，出版著作3部，在Adv. In Math., ARMA, SIAM J Math Anal, CPDE, J. Diff. Eqns等杂志发表SCI收录学术论文220余篇。