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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data
平滑数据 二维布西内斯 三维欧拉方程 稳定近似 自相似爆炸
2023/4/13
Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In this talk, we will first review recent progress in singu...
On asymptotics of a tracer advected in a locally self-similar,correlated flow
On asymptotics tracer advected locally self-similar correlated flow
2015/7/14
In this paper we consider the motion of a tracer in a flow that is locally self-similar and whose correlations decay at infinity but at the rate that does not guarantee that the flow does not have ”me...
Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions
Local-in-space estimates initial time weak solutions of the Navier-Stokes equations forward self-similar solutions Analysis of PDEs
2012/4/18
We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with $(-1)$-homogeneous initial data has a global scale-invariant solution which is smooth for positive time...
(Self-)similar groups and the Farrell-Jones conjectures
(Self-)similar groups the Farrell-Jones conjectures K-Theory and Homology
2011/9/21
Abstract: We show that contracting self-similar groups satisfy the Farrell-Jones conjectures as soon as their universal contracting cover is non-positively curved. This applies in particular to bounde...
An algorithm for computing the centered Hausdorff measure of self-similar sets
centered Hausdorff measure self-similar sets computability of fractal measures
2011/9/15
Abstract: We provide an algorithm for computing the centered Hausdorff measure of self-similar sets satisfying the strong separation condition. We prove the convergence of the algorithm and test its u...
Self-similar asymptotics of solutions to the Navier-Stokes system in two dimensional exterior domain
Self-similar asymptotics the Navier-Stokes system two dimensional exterior domain Analysis of PDEs
2011/9/1
Abstract: We consider the 2D incompressible Navier-Stokes equations with Dirichlet boundary condition in the exterior of one obstacle. Assuming that the circulation at infinity of the velocity is suff...
Semianalytic theory of self-similar optical propagation and mode locking using a shape-adaptive model pulse
adaptive model pulse Semianalytic theory self-similar optical propagation mode locking
2011/7/7
A semianalytic theory for the pulse dynamics in similariton amplifiers and lasers is presented, based on a model pulse with adaptive shape. By changing a single parameter, this test function can be co...
Singular integrals on self-similar sets and removability for Lipschitz harmonic functions in Heisenberg groups
Singular integrals self-similar sets removability Heisenberg group
2011/1/20
In this paper we study singular integrals on small (that is, measure zero and lower than full dimensional) subsets of metric groups. The main examples of the groups we have in mind are Euclidean space...
Exponential self similar solutions technique for instability phenomenon arising in double phase flow through porous medium with capillary pressure
Immiscible fluid Instability Flows in porous media
2010/9/25
The theoretical studies involved development of the differential equations which describe the instability of water by an oil-saturated rock. The basic assumption underlying the present investigation i...
Nontangential limits and Fatou-type theorems on post-critically finite self-similar sets
Fatou-type theorems post-critically finite self-similar sets
2010/11/18
In this paper we study the boundary limit properties of harmonic functions on $\mathbb R_+\times K$, the solutions $u(t,x)$ to the Poisson equation \[ \frac{\partial^2 u}{\partial t^2} + \Delta u = 0...
From Self-Similar Structures to Self-Similar Groups
From Self-Similar Structures Self-Similar Groups
2010/11/15
We explore the relationship between limit spaces of contracting self-similar groups and fractals. Exact conditions on a group are given under which its limit space has a self-similar structure and a ...
Heat conduction: a telegraph-type model with self-similar behavior of solutions II
Heat conduction telegraph-type model self-similar behavior of solutions II
2010/12/15
In our former study (J. Phys. A: Math. Theor. 43, (2010) 325210 or arXiv:1002.0999v1 [math-
ph]) we introduced a modified Fourier-Cattaneo law and derived a non-autonomous telegraph-type
heat conduc...
Estimates for the resolvent kernel of the Laplacian on p.c.f. self similar fractals and blowups
resolvent kernel Laplacian on p.c.f. self similar fractals blowups
2010/12/14
One of the main features of analysis on post-critically finite self-similar (pcfss) sets is
that it is possible to understand the behavior of the Laplacian and its inverse, the Green
operator, in te...
Lipschitz-Killing curvatures of self-similar random fractals
self-similar random fractals curvatures Minkowski content
2010/12/15
For a large class of self-similar random sets F in Rd geometric parameters Ck(F), k = 0, . . . , d, are introduced. They arise as a.s. (average or essential) limits of the volume Cd(F(")), the surface...
For a large class of self-similar sets F in Rd, analogues of the higher order mean curvatures
of differentiable submanifolds are introduced, in particular, the fractal Gauss-type curvature.
They are...