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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Global existence and decay of solutions to compressible Prandtl system with small analytic data
少量分析数据 可压缩 Prandtl系统解 全局存在 衰减
2023/4/18
In this talk, we shall prove the global existence and the large time decay estimate of solutions to compressible Prandtl system with small initial data, which is analytical in the tangential variable....
Electrified thin films:Global existence of non-negative solutions
Higher order equation Non-local equation Thin film equation Non-negative solutions
2015/10/15
We consider an equation modeling the evolution of a viscous liquid thin film wetting a horizontal solid substrate destabilized by an electric field normal to the substrate. The effects of the electric...
Global existence and blow-up phenomena for a periodic 2-component Camassa-Holm equation
A periodic 2-component Camassa-Holm equation global existence blow-up blow-up rate
2011/10/17
We first establish local well-posedness for a periodic 2-component Camassa-Holm equation. We then present two global existence results for strong solutions to the equation. We finally obtain several b...
Global existence of small amplitude solution to nonlinear system of wave and Klein-Gordon equations in four space-time dimensions
Global existence nonlinear system wave and Klein-Gordon equations four space-time dimensions
2011/9/14
Abstract: In this article one will develop a so-called hyperboloidal foliation method, which is an energy method based on a foliation of space-time into hyperboloidal hypersurfaces. This method permit...
On the wave-breaking phenomena and global existence for the generalized periodic Camassa-Holm equation
Generalized periodic Camassa-Holm equation Wave-breaking Global existence
2011/9/9
Abstract: Considered herein is the initial-value problem for the generalized periodic Camassa-Holm equation which is related to the Camassa-Holm equation and the Hunter-Saxton equation. Sufficient con...
Global existence and collisions for symmetric configurations of nearly parallel vortex filaments
Global existence and collisions parallel vortex filaments Analysis of PDEs
2011/9/1
Abstract: We consider the Schr\"odinger system with Newton-type interactions that was derived by R. Klein, A. Majda and K. Damodaran [18] to modelize the dynamics of N nearly parallel vortex filaments...
Global existence for the Euler-Maxwell system
Global existence the Euler-Maxwell system Analysis of PDEs
2011/8/30
Abstract: The Euler-Maxwell system describes the evolution of a plasma when the collisions are important enough that each species is in a hydrodynamic equilibrium. In this paper we prove global existe...
The global existence of the smoothing solution for the Navier-Stokes equations
smoothing solution Poisson’s equation heat-conduct equation the Schauder fixed-point theorem
2011/8/24
Abstract: This paper discussed the global existence of the smoothing solution for the Navier-Stokes equations. At first, we construct the theory of the linear equations which is about the unknown four...
Blow-up phenomena and global existence for a periodic two-component Hunter-Saxton system
A periodic two-component Hunter-Saxton system blow-up scenario blow-up
2011/2/28
This paper is concerned with blow-up phenomena and global existence for a periodic two-component Hunter-Saxton system. We first derive precise blow-up scenarios for strong solutions to the system. The...
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...
The Null Condition and Global Existence for Nonlinear Wave Equations on Slowly Rotating Kerr Spacetimes
Null Condition Global Existence Nonlinear Wave Equations Rotating Kerr Spacetimes
2010/12/16
We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in tim...
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 ...
Global existence for the generalized two-component Hunter-Saxton system
Generalized Hunter-Saxton system global existence blow-up scenario
2010/12/1
e study the global existence of solutions to a two-component generalized Hunter-Saxton system in the periodic setting. We first prove a persistence result of the solutions. Then for some particular ch...
Global existence of solutions for some coupled systems of reaction-diffusion equations
Reaction-Diffusion systems Global Existence Lyapunov Functional
2010/12/14
The aim of this work is to study the global existence of solutions for some coupled systems of reaction diffusion which describe the spread within a population of infectious disease. We consider a tri...
Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations
Nonlocal Cauchy problem Boussinesq equation Global existence Blow-up
2010/12/1
We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonne...