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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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Type II blowup solutions to the 5D semilinear heat equation with double power nonlinearity
双幂非线性 5D 双线性热方程 II型爆破解
2023/5/16
We will discuss the existence of blowup solutions to $u_t=\Delta u+|u|^\frac{4}{n-2}u-|u|^{q-1}u$ with $0ow that there are three kinds of blowup solutions in this equation. I...
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...
Dynamics near the threshold for blowup in the one-dimensional focusing nonlinear Klein-Gordon equation
threshold for blowup one-dimensional nonlinear Klein-Gordon equation
2011/1/18
We study dynamics near the threshold for blowup in the focusing nonlinear Klein-Gordon equa-
tion utt −uxx +u−|u|2 u = 0 on the line. Using mixed numerical and analytical methods we find
...
Blowup for the C^1 Solutions of the Euler-Poisson Equations of Gaseous Stars in R^N
C^1 Solutions Euler-Poisson Equations Gaseous Stars
2011/2/25
The Newtonian Euler-Poisson equations with attractive forces are the classical models for
the evolution of gaseous stars and galaxies in astrophysics. In this paper, we use the integration method to ...
Perturbational Blowup Solutions to the 2-Component Camassa-Holm Equations
Perturbational Blowup 2-Component Camassa-Holm Equations
2011/1/19
In this article, we study the perturbational method to construct the non-radially symmet-ric solutions of the compressible 2-component Camassa-Holm equations. In detail, we first combine the substitut...
Blowup for the Euler and Euler-Poisson Equations with Repulsive Forces II
Blowup Euler and Euler-Poisson Equations Repulsive Forces II
2011/2/25
In this paper, we continue to study the blowup problem of the N-dimensional compressible
Euler or Euler-Poisson equations with repulsive forces, in radial symmetry. In details, we
extend the recent ...
Perturbational Blowup Solutions to the 1-dimensional Compressible Euler Equations
Perturbational Blowup 1-dimensional Compressible Euler Equations
2011/1/20
We study the construction of analytical non-radially solutions for the 1-dimensional com-pressible adiabatic Euler equations in this article. We could design the perturbational method
to construct a ...
Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation
the blowup/global existence dichotomy the focusing cubic nonlinear Klein-Gordon equation
2010/11/15
We present some numerical findings concerning the nature of the blowup vs. global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation in three dimensions for radial data. The co...
This short paper is dedicated to Mauricio Peixoto who abstracted the practical theory of ODE's and to David Rand who applied the subsequent powerful abstract theory to practical problems.
On the Global Existence and Blowup Phenomena of Schrödinger Equations with Multiple Nonlinearities
Nonlinear Schr¨odinger equation Global existence Blow up in Nonlinear Schr¨odinger equation Global existence
2010/11/29
In this paper, we consider the global existence and blowup phenomena of the following Cauchy problem−iut = u − V (x)u + f(x, |u|2)u + (W ⋆ |u|2)u, x ∈ RN, t > 0,u(x, 0) = u0(x), x ...