In this talk we discuss an existence result regarding bounded-energy weak-solutions for the quasi-stationary compressible Stokes equations. This system arises for instance in biology, porous media, supra-conductivity or other applications in the low Reynolds number regime. These equations are formally obtained from the Navier-Stokes system for a compressible barotropic fluid by discarding the convective terms from the momentum equation.

We present a method to study global strong solutions of partially dissipative hyperbolic systems in a critical regularity setting. Introducing hybrid Besov norms, with different regularity exponents in low and high frequency, we pinpoint optimal smallness conditions for global well-posedness and get more accurate information on the qualitative properties of the constructed solutions.To handle the high frequencies of the solution, our analysis relies on the construction of a Lyapunov functional in the spirit of the one constructed by Beauchard and Zuazua (ARMA 2011). And concerning the low frequencies, exhibiting a damped mode with faster time decay than the whole solution plays a key role.

We prove that, among all open substacks of moduli stacks of rank 2 bundles over a curve, the open substack of semi-stable bundles is the unique maximal one that admits a separated good moduli space. One example in rank 3 case shows that a s...

In this talk, we start with recalling the double centralizer property in a graduate algebra course, then review its origin where Schur completely determined the polynomial representations of GL(n,$\mathbb{C}$) via the technique in 1927, ...

In this talk, for one-dimension systems of quasilinear wave equations with null conditions, we will introduce the following results:1.  Global existence of classical solutions for the Cauchy problem in the small data setting;...

In this report, we introduce some recent works on the Euler sums via the Stirling sums, multiple zeta values, residue computation, etc. We also establish several series identities on the Euler type sums, which can be viewed as symmet...

In this talk, we will discuss the $L_p$ Brunn-Minkowski theory associated with the $C$-coconvex sets for $p\in [0,1)$ and the $L_p$ Minkowski problem associated with the $C$-coconvex sets for $p\in R$. In particular, we will talk about ou...

It is an important problem in the theory of modular forms to determine the structure of rings of modular forms, that is, to find explicit generators and their relations. In this talk, I will introduce the modular Jacobian approach to construct and cla...

In this talk we report our series of results on minimal graphs and related problems in warped product (WP) manifolds. Our motivation is to view WP manifolds as canonical manifolds in the certain sense. Then we introduce our result...

In this talk, I shall first discuss a newly developed multi-modes Monte Carlo method for solving random PDEs, both random diffusion equations and random wave equations (in frequency domain) will ...