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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...
In this talk, I will discuss the method of convex integration and its applications on non-uniqueness of weak solutions to the hyper-viscous incompressible Navier-Stokes equations as well as the hypo-v...
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...
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...
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...
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...
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...
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...
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...
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...
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...
This work is focused on the solvability of initial-boundary value problems for degenerate parabolic partial differential equations that arise in the pricing of Asian options, and on the investigation...
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...
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...
期刊信息 篇名 Global Existence and Asymptotic Limits of Weak Solutions of the Bipolar Hydrodynamic Model for Semiconductors 语种 英文 撰写或编译 撰写 作者 Norbert J. Mauser,Youchun Qiu,Kai-Jun Zhang 第一作者单位 东北师范大学 刊物名称 M...

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