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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Global well-posedness of the 1d compressible Navier-Stokes system with rough data
粗略数据 一维可压缩 纳维-斯托克斯系统 全局适定性
2023/4/24
We study the global well-posedness problem for the 1d compressible Navier-Stokes systems (cNSE) in gas dynamics with rough initial data. First, Liu and Yu (Commun Pure Appl Math 75(2):223-348, 2022) e...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Global well-posedness of the 1d compressible Navier-Stokes system with rough data
粗略数据 一维可压缩 纳维-斯托克斯系统 全局适定性
2023/4/24
We study the global well-posedness problem for the 1d compressible Navier-Stokes systems (cNSE) in gas dynamics with rough initial data. First, Liu and Yu (Commun Pure Appl Math 75(2):223-348, 2022) e...
Global well-posedness and stability of electro-kinetic flows
Navier-Stokes-Nernst-Planck-Poisson equations local and global well-posedness exponential stability of steady states
2012/6/27
We consider a coupled system of Navier-Stokes and Nernst-Planck equations, describing the evolution of the velocity and the concentration fields of dissolved constituents in an electrolyte solution. M...
Global well-posedness for the Kawahara equation with low regularity data
Kawahara equation global well-posedness Cauchy problem I-method
2012/3/1
We consider the global well-posedness for the Cauchy probelem of the Kawahara equation which is one of the fifth order KdV type equations. We first establish the local well-posedness in a more suitabl...
Global well-posedness and scattering for Skyrme wave maps
Wave maps Skyrme model Adkins-Nappi model global existence scattering theory
2011/7/28
Abstract: We study equivariant maps corresponding to the classical Skyrme model and the Adkins-Nappi model, for which we prove global existence and scattering in critical Sobolev-Besov spaces.
Global well-posedness and scattering for the defocusing cubic NLS in four dimensions
Global well-posedness scattering the defocusing cubic NLS
2010/11/11
In this short note we present a new proof of the global well-posedness and scattering result for the defocusing energy-critical NLS in four space dimensions obtained previously by Ryckman and Visan. ...
Local and Global Well-Posedness for Aggregation Equations and Patlak-Keller-Segel Models with Degenerate Diffusion
Local Global Well-Posedness Aggregation Equations Patlak-Keller-Segel Models Degenerate Diffusion
2010/12/6
Recently, there has been a wide interest in the study of aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper is the unification...
The supercritical generalized KdV equation: Global well-posedness in the energy space and below
supercritical generalized KdV equation Global well-posedness energy space and below
2010/12/8
We consider the generalized Korteweg-de Vries (gKdV) equation @tu + @3 xu + μ@x(uk+1) = 0, where k ≥ 5 is an integer number and μ = ±1.In the focusing case (μ = 1), we show that if the initial data u0...
Global well-posedness for a Smoluchowski equation coupled with Navier-Stokes equations in 2D
Nonlinear Fokker-Planck equations Navier-Stokes equations Smoluchowski equation micro-macro interactions
2014/4/4
We prove global existence for a nonlinear Smoluchowski equation (a nonlinear FokkerPlanck equation) coupled with Navier-Stokes equations in 2d. The proof uses a deteriorating regularity estimate in th...