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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
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...
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
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
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...
Weak solutions to lubrication equations in the presence of strong slippage
Weak solutions lubrication equations presence of strong slippage
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...
H¨older continuity of the weak solutions for parabolic equations with the nonstandard growth condition
Boundedness H\
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...