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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：C1,1/3- very weak solutions to the two dimensional Monge–Ampère equation
二维 Monge–Ampère方程 C1,1/3极弱解
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2023/11/29
For any θ<1/3 , we show that very weak solutions to the two-dimensional Monge–Ampère equation with regularity C1,θ are dense in the space of continuous functions. This result is shown by a convex inte...
Global weak solutions for a Vlasov-Fokker-Planck/Navier-Stokes system of equations
Global weak solutions Vlasov-Fokker-Planck Navier-Stokes system of equations
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2015/10/15
We establish the existence of a weak solutions for a coupled system of kinetic and fluid equations. More precisely, we consider a Vlasov-FokkerPlanck equation coupled to compressible Navier-Stokes equ...
EXISTENCE OF WEAK SOLUTIONS TO KINETIC FLOCKING MODELS
flocking kinetic equations existence velocity averaging CuckerSmale self-organized dynamics
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2015/10/15
We establish the global existence of weak solutions to a class of kinetic flocking equations. The models under conideration include the kinetic Cucker-Smale equation [6, 7] with possibly non-symmetric...
Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions
Local-in-space estimates initial time weak solutions of the Navier-Stokes equations forward self-similar solutions Analysis of PDEs
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2012/4/18
We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with $(-1)$-homogeneous initial data has a global scale-invariant solution which is smooth for positive time...
On the existence of weak solutions to the three-dimensional steady compressible Navier-Stokes equations in bounded domains
Steady compressible Navier-Stokes equations existence for any γ > 1 weighted estimate bounded domains
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2011/9/22
Abstract: We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio \gamma > 1. Generally...
Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system
Vlasov-Darwin weak solutions uniqueness optimal transportation
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2011/9/20
Abstract: We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by Loeper in...
Global Classical and Weak Solutions to the Three-Dimensional Full Compressible Navier-Stokes System with Vacuum and Large Oscillations
Global Classical Weak Solutions Three-Dimensional Full Compressible Navier-Stokes System Vacuum and Large Oscillations
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2011/9/19
Abstract: We establish the global existence and uniqueness of classical solutions to the three-dimensional full compressible Navier-Stokes system with smooth initial data which are of small energy but...
Weak solutions to lubrication equations in the presence of strong slippage
Weak solutions lubrication equations presence of strong slippage
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2011/1/18
The existence of global weak solutions is proved for one-dimensional lubrication models that describe the dewetting process of nanoscopic thin polymer films on hy-drophobyzed substrates and take accou...
Existence of global weak solutions for Navier-Stokes equations with large flux
Navier-Stokes equation weighted Sobolev spaces Neumann boundary-value problem
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2010/12/14
Global existence of weak solutions to the Navier-Stokes equation in a cylindrical domain under the slip boundary conditions and with inflow and outflow was proved. To prove the energy estimate, crucia...
Eastern Boundary Conditions and Weak Solutions of the Ideal Thermocline Equations
Boundary Conditions Weak Solutions Ideal Thermocline Equations
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2009/1/13
It is argued that the ideal fluid thermocline equations have “weak” (i.e., nondifferentiable) solutions that satisfy no mass-flux boundary conditions at the East. This conclusion is based on a local a...
H¨older continuity of the weak solutions for parabolic equations with the nonstandard growth condition
Boundedness H\
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2007/12/12
In this paper, we investigate the interior regularity including the local boundedness and the interior H\"{o}lder continuity of weak solutions for parabolic equations of the $p(x,t)$-Laplacian type. W...
WEAK SOLUTIONS TO THE TWO-DIMENSIONAL DERIVATIVE GINZBURG-LANDAU EQUATION
Global weak solution approxim
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2007/12/11
In this paper, we deal with the generalized derivative Ginzburg-Landau equation in two spatial dimensions, and obtain the existence of global weak solutions for this equation subject to periodic bound...