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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the L2 rate of convergence in the limit from the Hartree to the Vlasov–Poisson Equation
哈特里到弗拉索夫 泊松方程 极限 L2收敛率
2023/4/13
We consider the semiclassical limit from the Hartree equation with Coulomb interaction potential to the Vlasov–Poisson equation. Using a new stability estimate for the difference of the square roots o...
One of the major discoveries of the 20th century mathematics is
the possibility of random behavior of deterministic systems. There is
a hierarchy of chaotic properties for a dynamical systems but on...
We consider a large class of partially hyperbolic systems containing, among others, ane maps, frame
ows on negatively curved manifolds and mostly contracting di eomorphisms.
If the rate of mixing ...
Inviscid limit for axisymmetric stratified Navier-Stokes system
Inviscid limit axisymmetric stratified Navier-Stokes system Analysis of PDEs
2012/6/21
This paper is devoted to the study of the Cauchy problem for the stratified Navier-Stokes system in space dimension three. In the first part of the paper, we prove the existence of a unique global sol...
On the inviscid limit of the system "viscous incompressible fluid + rigid body" with the Navier conditions
inviscid limit of the system viscous incompressible fluid Navier conditions Analysis of PDEs
2012/6/6
In this paper we consider the inviscid limit for the system "viscous incompressible fluid + rigid body" in $\R^{3}$ when some Navier slip conditions are prescribed on the body's boundary. We prove the...
Spectral stability of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation in the Korteweg-de Vries limit
Spectral stability periodic wave trains Korteweg-de Vries/Kuramoto-Sivashinsky equation Korteweg-de Vries limit
2012/3/1
We study the spectral stability of a family of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation $ \partial_t v+v\partial_x v+\partial_x^3 v+\delta(\partial_x^2 v +\partial_x...
Singular limit and exact decay rate of a nonlinear elliptic equation
existence of solution nonlinear elliptic equations singular limit exact decay rate Yamabe flow
2011/9/6
Abstract: For any $n\ge 3$, $00$, $\beta>0$, $\alpha$, satisfying $\alpha\le\beta(n-2)/m$, we prove the existence of radially symmetric solution of $\frac{n-1}{m}\D...
Semiclassical limit for generalized KdV equations before the gradient catastrophe
Semiclassical limit generalized KdV equations the gradient catastrophe Analysis of PDEs
2011/8/24
Abstract: We study the semiclassical limit of the (generalised) KdV equation, for initial data with Sobolev regularity, before the time of the gradient catastrophe of the limit conservation law. In pa...
Semiclassical limit for the nonlinear Klein Gordon equation in bounded domains
Klein Gordon Equation Semiclassical Limit Variational Methods Nonlinear Equations
2011/2/28
We are interested to the existence of standing waves for the nonlinear Klein Gordon equation "2 + W′( ) = 0 in a bounded domain D.
For any m > 1, we construct properly embedded minimal surfaces in H2 R with genus zero,
infinitely many vertical planar ends and m limit ends. We also provide examples with an infinite countable nu...
Vanishing Viscosity Limit for Isentropic Navier-Stokes Equations with Density-dependent Viscosity
compressible Navier-Stokes compressible Euler equations
2010/12/9
In this paper, we study the vanishing viscosity limit of one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity, to the isen-tropic compressible Euler equatio...
The semiclassical limit of eigenfunctions of the Schrödinger equation and the Bohr-Sommerfeld quantization condition, revisited
he semiclassical limit of eigenfunctions Schrö dinger equation Bohr-Sommerfeld quantization condition
2010/12/1
Consider the semiclassical limit, as the Planck constant ~ ! 0, of bound states of a quantum particle in a one-dimensional potential well. We justify the semiclassical asymptotics of eigenfunctions an...
A scaling limit theorem for the parabolic Anderson model with exponential potential
scaling limit theorem parabolic Anderson model exponential potential
2010/12/13
The parabolic Anderson problem is the Cauchy problem for the heat equation ¶tu(t, z) = D u(t, z)+x (t, z)u(t, z) on (0,¥)×Zd with random potential (x (t, z) : z ∈ Zd ) and localized initial c...