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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...
A natural smooth compactiffcation of the space of elliptic curves in projective space via blowing up the space of stable maps
projective space stable maps
2015/7/14
We nd it interesting that such a natural naive approach as we will describe
actually works, and yields a desingularization with these nice properties.
Singular parabolic p-Laplacian systems under non-smooth external forces. Regularity up to the boundary
Initial-boundary value problems p-Laplacian parabolic singular systems regularity up to the boundary
2012/6/30
We study the regularity of the solutions to initial-boundary value problems for N-systems of the p-Laplacian type, in $n\geq 3$ space variables, with square-integrable external forces in the space-tim...
Reconstruction of a piecewise smooth absorption coefficient by an acousto-optic process
acousto-optic inverse problem spherical Radon transform Helmholtz decomposition piecewise smooth functions reconstruction Landweber iteration stability
2012/6/27
The aim of this paper is to tackle the nonlinear optical reconstruction problem. Given a set of acousto-optic measurements, we develop a mathematical framework for the reconstruction problem in the ca...
Wave equations on non-smooth space-times
Wave equation, Cauchy problem, global hyperbolicity, distributional solutions, generalized solutions
2011/8/22
Abstract: We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distr...
Smooth Contractive Embeddings and Application to Feynman Formula for Parabolic Equations on Smooth Bounded Domains
Smooth contractive extension operator elliptic differential operator
2011/1/18
We prove two assumptions made in an article by Ya.A. Butko, M. Grothaus,O.G. Smolyanov concerning the existence of a strongly continuous operator semi-group solving a Cauchy-Dirichlet problem for an e...
Weighted maximal regularity estimates and solvability of non-smooth elliptic systems II
elliptic system conjugate function maximal regularity
2011/1/19
In this article, we continue the development of new solvability meth-ods for boundary value problems of Dirichlet, regularity, Neumann type with square integrable data for divergence form second order...
On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds
isolated curves deformations Hilbert schemes Calabi-Yau threefolds
2010/12/10
Building on results of Clemens and Kley, we find criteria for a continuous family of curves in a nodal K-trivial threefold Y0 to deform to a scheme of finitely many smooth isolated curves in a general...
Anticipative Stochastic Differential Equations with Non-smooth Diffusion Coefficient
Non-smooth and anticipative stochastic differential equations Skorohod integral Malliavin derivative
2007/12/11
In this paper we prove the existence and uniqueness of the solutions to the one-dimensional linear stochastic differential equation with Skorohod integral $$\ \ X_t(\omega )=\eta (\omega )+ \int^t_0 a...