理学院：On the global regularity of a Helical-Decimated version of the 3D Navier-Stokes equations

报告题目：On the global regularity of a Helical-Decimated version of the 3D Navier-Stokes equations  

报告人:Prof. Luca Biferale

       Dept. Physics and CAST

       (Centre for Applications of Calculus to Science and Technology)

       University of Rome “Tor Vergata”, Italy

时间：2018年3月27日 14:00

地点： 江宁校区励学楼B 219

Abstract: We study the global regularity, for all time and all initial data in H^{1/2}, of a recently introduced decimated version of the incompressible 3D Navier-Stokes (dNS) equations. The model is based on a projection of the dynamical evolution of Navier-Stokes (NS) equations into the subspace where helicity (the L^2-scalar product of velocity and vorticity) is sign-definite. The presence of a second (beside energy) sign-definite inviscid conserved quadratic quantity, which is equivalent to the H^{1/2}-Sobolev norm, allows us to demonstrate global existence and uniqueness, of space-periodic solutions, together with continuity with respect to the initial conditions, for this decimated 3D model. This is achieved thanks to the establishment of two new estimates, for this 3D model, which show that the H1/2 and the time average of the square of the H^{3/2} norms of the velocity field remain finite. Such two additional bounds are known, in the spirit of the work of H.Fujita and T.Kato (Arch.Ration. Mech. Anal. 16:269–315, 1964; Rend. Semin. Mat. Univ. Padova 32:243–260, 1962), to be sufficient for showing well-posedness for the 3D NS equations. Furthermore, they are directly linked to the helicity evolution for the dNS model, and therefore with a clear physical meaning and consequences.

报告人简介:Luca Biferale教授现任意大利罗马大学物理系全职教授，是世界知名的湍流研究专家。Biferale教授于1993年于罗马大学获得博士学位，1995年至2004年任罗马大学物理学院研究员，2005年至2014年任罗马大学物理系副教授，2014年至今任罗马大学全职教授。Biferale教授于2008年当选美国物理学会会士，2010年当选欧洲力学学会会士，并于2013年获欧洲研究协会高等研究计划项目支持。2007年至2013年任《Physical Review Letters》副编辑。至今已发表学术论文220余篇。