|Eugene Tyrtyshnikov||INM RAS, Moscow|
Bio: Marchuk Institute of Numerical Mathematics of RAS, director, Academician of RAS.
Tikhonov's solution to a class of linear systems equivalent within perturbations.
A standard approach to incorrect problems suggests that a problem of interest is reformulated with the knowledge of some additional a priori information. This can be done by several well-known regularization techniques. Many practical problems are successfully solved on this way. What does not still look as completely satisfactory is that the new reset problem seems to appear rather implicitly in the very process of its solution.
In 1980, A.N. Tikhonov proposed a reformulation that arises explicitly before the discussion of the solution methods. He suggested a notion of normal solution to a family of linear algebraic systems described by a given individual system and its vicinity comprising perturbed systems, under the assumption that there are compatible systems in the class notwithstanding the compatibility property of the given individual system. Tikhonov proved that the normal solution exists and unique. However, a natural queston about the correctness of the reset problem was not answered. In this talk we address a question of correctness of the reformulated incorrect problems that seems to have been missed in all previous considerations. The main result is the proof of correctness for Tikhonov's normal solution. Possible generalizations and diffculties will be also discussed.
|Zhen Lei||Chern Institute of Mathematics, Nankai University|
Bio: Dr. Zhen Lei is a distinguished professor of School of Mathematical Sciences at Fudan University. His honors include: Second-prize Winner of the National Prize of Natural Sciences; Winner of Shanghai Peony Prize of Natural Science; National Science Foundation for Distinguished Young Scholars; Changjiang Distinguished Professor; National Special Support Program for Leading Talents in Science and Technology Innovation. He is the Vice President of China Society for Industry and Applied Mathematics. Professor Lei's research is focused on the theory of PDEs arising from fluid mechanics and methematical physics. He introduced the concept of strong null condition and proved the global well-posedness of classical solutions to the incompressible elastodynamics in 2D. He has also made significant contributions to the well-posedness theory and Liouville properties of the incompressible Navier-Stokesequations. Professor Lei holds the position of associate editor-in-chief of Chinese Annals of Mathematics; associate editor-in-chief of Journal of Fudan University (Natural Science). He also serves at the editorial board for several academic journals, such as Communications in Mathematical Sciences, Communications on Pure and Applied Mathematics, Fundamental Research, etc.
Liouville Properties of the Incompressible Navier-Stokes Equations.
In this talk we will report recent results on the Liouville properties of bounded ancient solutions to the three-dimensional incompressible Navier-Stokes equations. These properties are crucial for excluding potential type I singularities or understanding the structure of possible singulairites of local smooth solutions of the corresponding Cauchy problem.
The meeting will be held in the form of a webinar on the Zoom platform.
Pre-registration for the event is not required.
To join Zoom meeting（You can join in the meeting without a phone number):
Meeting ID : 822 3903 4166