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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：No blow-up by nonlinear It? noise for the Euler equations
非线性 爆炸 欧拉方程 噪声
2023/5/17
We consider the incompressible Euler equations in two or three dimensions and we show that the addition of a suitable multiplicative It? noise with superlinear growth prevents a smooth solution from b...
On the blow-up set of the Yang–Mills flow on Kahler surfaces
blow-up set Yang–Mills flow Kahler surfaces
2015/12/17
The Yang–Mills flow on a Kahler surface with holomorphic initial data converges smoothly away from a singular set determined by the Harder–Narasimhan–Seshadri filtration of the initial holomorphic bun...
Existence and Blow-Up Behavior for Solutions of the Generalized Jang Equation
Existence and Blow-Up Behavior Solutions of the Generalized Jang Equation Differential Geometry
2012/6/9
The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study o...
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...
Generalized convexity and the existence of finite time blow-up solutions for an evolutionary problem
Finite time blow-up solutions p-Laplacian generalized convexity regularly varying functions
2011/9/22
Abstract: In this paper we study a class of nonlinearities for which a nonlocal parabolic equation with Neumann-Robin boundary conditions, for $p$-Laplacian, has finite time blow-up solutions.
A Blow-up Criterion for Two Dimensional Compressible Viscous Heat-Conductive Flows
Blow-up Criterion Two Dimensional Compressible Viscous Heat-Conductive Flows Analysis of PDEs
2011/9/19
Abstract: We establish a blow-up criterion in terms of the upper bound of the density and temperature for the strong solution to 2D compressible viscous heat-conductive flows. The initial vacuum is al...
Generalized blow-up of corners and fiber products
Generalized blow-up corners and fiber products Geometric Topology
2011/9/13
Abstract: Radial blow-up, including inhomogeneous versions, of boundary faces of a manifold (always with corners) is an important tool for resolving singularities, degeneracies and competing notions o...
Boundary Characteristic Point Regularity for Navier-Stokes Equations: Blow-up Scaling and Petrovskii-type Criterion (a Formal Approach)
Navier–Stokes equations in R3 backward paraboloid characteristic vertex boundary regularity blow-up scaling boundary layer
2011/9/6
Abstract: It is shown that Wiener's regularity of the vertex of a backward paraboloid for 3D Navier-Stokes equations with zero Dirichlet conditions on the paraboloid boundary is given by Petrovskii's ...
The blow-up theorem of a discrete semilinear wave equation
The blow-up theorem semilinear wave equation Analysis of PDEs
2011/9/1
Abstract: In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear wave equa...
b-Stability and blow-ups
b-Stability and blow-ups Differential Geometry Algebraic Geometry
2011/8/31
Abstract: We extend an argument of Stoppa to make some prgress towards a proof that K\"ahler-Einstein manifolds are "b-stable". We point out some algebro-geometric questions, involving finite generati...
On the Wu classes of the topological blow up
Wu class Steenrod operation Topological blow up
2011/8/26
Abstract: We mainly discuss the Wu classes $v(M)$ and the Steenrod operation $Sq$ of the topological blow up $\tilde{M}$. The formula of the Wu class $v(\tilde{M})$ will be given as well as the formul...
Blow-up time for a semilinear parabolic equation with variable reaction
Semilinear parabolic equation blow-up numerical blow-up time
2011/4/6
In this paper, we address the solution of a semilinear heat equation with variable reaction subject to Dirichlet boundary conditions and nonnegative initial datum. Under some assumptions, we show that...
Lagrangian blow-ups, blow-downs, and applications to real packing
Lagrangian blow-ups blow-downs applications real packing
2011/1/18
Given a symplectic manifold (M; !) and a Lagrangian submanifold L, we construct versions of the symplectic blow-up and blow-down which are defined relative to L.
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...
Blow-up for a degenerate and singular parabolic system with nonlocal sources and absorptions
Degenerate and singular parabolic system blow up blow-up set
2010/11/1
This paper deals with the blow-up properties of the solution to the degenerate and singular parabolic system with nonlocal sources, absorptions and homogeneous Dirichlet boundary conditions. The exist...