Department of Analysis

(S^3) Summer Seminar and School lần 3,

từ ngày 23 - 07 đến 30 - 07 - 2016, tại P421, T1 Builidng, ĐH KHTN Hà Nội

bao gồm Workshop và Trường hè. Mục tiêu là tạo môi trường giao lưu, động viên các bạn trẻ trong các lĩnh vực nghiên cứu Giải tích thực, Giải tích phức, Phương trình đạo hàm riêng và các vấn đề liên quan. S^3 rất mong các bạn trẻ đang tích cực nghiên cứu về tham gia và báo cáo tại S^3.

S^3 bao gồm:

Summer Seminar

The main purpose in this talk is to give a brief survey on the tangential Cauchy-Riemann equations on pseudoconvex boundaries in $\mathbb C^2$. The content includes two parts: boundary regularities for solutions to the equation and their applications to prescribing zeros of holomorphic functions. Both of them will be considered on a  class of pseudoconvex boundaries of finite and infinite type in the sense of Range.

Báo cáo trình bày dáng điệu định tính của điểm cân bằng của một số phương trình và hệ phương trình sai phân phi tuyến.

In this talk, we construct a real hypersurface germ $(M,0)$ of infinite type in the sense of D'Angelo that does not admit any holomorphic curve that has infinite order contact with $M$ at $0$. This is a joint work with Nguyen Ngoc Khanh.

We give some versions of Lojasiewicz inequalities on non-compact sets for some polynomial and semialgebraic functions with explicit exponents. More precisely, we give some necessary and sufficient conditions for which Lojasiewicz inequalities exists on some domains which are not compact. Moreover, under some conditions of non-degeneracy at infinity, all the Lojasiewicz exponents can be estimated.

For time-varying non-regressive linear dynamic equations on a time scale with bounded graininess, we introduce a concept of dominated splitting or exponential separation which is weaker than exponential dichotomy. Next, a characterization of dominated splitting is obtained in terms of exponential dichotomy of rescaling dynamic equations. As a consequence, we get roughness of dominated splitting. Finally, it is shown that there is a unique minimal decomposition into exponentially separated subspaces.

In this talk, we present stability of bounded or almost periodic mild solutions for the Navier-Stokes-Oseen equation, this equation describes flows of incompressible viscous fluid around a translational and rotational obstacle with the complement being an exterior domain.