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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 fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices
Elliptic equations Fast algorithms Nested dissection Hierarchical matrices Sparse matrix
2015/7/14
We present a fast algorithm for solutions to linear systems arising from three dimensional elliptic problems on a regular Cartesian mesh. We follow the approach of Schmitz and Ying (2012) on combining...
On a 3D isothermal model for nematic liquid crystals accounting for stretching terms
3D isothermal model nematic liquid crystals Analysis of PDEs
2011/9/15
Abstract: The present contribution investigates the well-posedness of a PDE system describing the evolution of a nematic liquid crystal flow under kinematic transports for molecules of different shape...
On the Local Well-posedness of a 3D Model for Incompressible Navier-Stokes Equations with Partial Viscosity
3D Model Incompressible Navier-Stokes Equations Partial Viscosity Analysis of PDEs
2011/8/31
Abstract: In this short note, we study the local well-posedness of a 3D model for incompressible Navier-Stokes equations with partial viscosity. This model was originally proposed by Hou-Lei in \cite{...
A lower bound on blowup rates for the 3D incompressible Euler equation and a single exponential Beale-Kato-Majda estimate
lower bound blowup rates 3D incompressible Euler exponential Beale-Kato-Majda estimate
2011/8/23
Abstract: We prove a Beale-Kato-Majda criterion for the loss of regularity for solutions of the incompressible Euler equations in $H^{s}(\R^3)$, for $s>\frac52$. Instead of double exponential estimate...
Coherent vortex structures and 3D enstrophy cascade
Coherent vortex structures 3D enstrophy cascade
2011/8/22
Abstract: Existence of 2D enstrophy cascade in a suitable mathematical setting, and under suitable conditions compatible with 2D turbulence phenomenology, is known both in the Fourier and in the physi...