In this paper, the Dirichlet problem of Stokes approximate of non-homogeneous incompressible Navier-Stokes equations is studied. It is shown that there exist global weak solutions as well as global and unique strong s...In this paper, the Dirichlet problem of Stokes approximate of non-homogeneous incompressible Navier-Stokes equations is studied. It is shown that there exist global weak solutions as well as global and unique strong solution for this problem, under the assumption that initial density po（x） is bounded away from 0 and other appropriate assumptions （see Theorem 1 and Theorem 2）. The semi-Galerkin method is applied to construct the approximate solutions and a prior estimates are made to elaborate upon the compactness of the approximate solutions.展开更多
We prove the global existence and uniqueness of admissible weak solutions to an asymptotic equation of a nonlinear hyperbolic variational wave equation with nonnegative L^2(R) initial data.
This work consider boundary integrability of the weak solutions of a non-Newtonian compressible fluids in a bounded domain in dimension three, which has the constitutive equartions as ■The existence result of weak so...This work consider boundary integrability of the weak solutions of a non-Newtonian compressible fluids in a bounded domain in dimension three, which has the constitutive equartions as ■The existence result of weak solutions can be get based on Galerkin approximation. With the linear operator B constructed by BOGOVSKII, we show that the density ■is square integrable up to the boundary.展开更多
In this paper, we study the ill posed Perona-Malik equation of image processing[14] and the regularized P-M model i.e. C-model proposed by Catte et al.[4]. The authors present the convex compound of these two models i...In this paper, we study the ill posed Perona-Malik equation of image processing[14] and the regularized P-M model i.e. C-model proposed by Catte et al.[4]. The authors present the convex compound of these two models in the form of the system of partial differential equations. The weak solution for the equations is proved in detail. The additive operator splitting （AOS） algorithm for the proposed model is also given. Finally, we show some numeric experimental results on images.展开更多
In this paper, we study a free boundary value problem for two-phase liquid- gas model with mass-dependent viscosity coefficient when both the initial liquid and gas masses connect to vacuum continuously. The gas is as...In this paper, we study a free boundary value problem for two-phase liquid- gas model with mass-dependent viscosity coefficient when both the initial liquid and gas masses connect to vacuum continuously. The gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid. We give the proof of the global existence and uniqueness of weak solutions whenβ∈ （0, 1）, which have improved the result of Evje and Karlsen, and we obtain the regularity of the solutions by energy method.展开更多
基金the National Natural Science Foundation of China(No.10431060)
文摘In this paper, the Dirichlet problem of Stokes approximate of non-homogeneous incompressible Navier-Stokes equations is studied. It is shown that there exist global weak solutions as well as global and unique strong solution for this problem, under the assumption that initial density po（x） is bounded away from 0 and other appropriate assumptions （see Theorem 1 and Theorem 2）. The semi-Galerkin method is applied to construct the approximate solutions and a prior estimates are made to elaborate upon the compactness of the approximate solutions.
基金The work of Ping Zhang is supported by the Chinese postdoctor's foundation,and that of Yuxi Zheng is supported in part by NSF DMS-9703711 and the Alfred P.Sloan Research Fellows award
文摘We prove the global existence and uniqueness of admissible weak solutions to an asymptotic equation of a nonlinear hyperbolic variational wave equation with nonnegative L^2(R) initial data.
基金supported by the National Natural Science Foundation of China(11271305,11531010)
文摘This work consider boundary integrability of the weak solutions of a non-Newtonian compressible fluids in a bounded domain in dimension three, which has the constitutive equartions as ■The existence result of weak solutions can be get based on Galerkin approximation. With the linear operator B constructed by BOGOVSKII, we show that the density ■is square integrable up to the boundary.
基金Supported in part by the National Natural Science Foundation of China under Grant(No.11571325,No.11271126)Science Research Project of CUC under Grant No.3132016XNL1612
文摘In this paper, we study the ill posed Perona-Malik equation of image processing[14] and the regularized P-M model i.e. C-model proposed by Catte et al.[4]. The authors present the convex compound of these two models in the form of the system of partial differential equations. The weak solution for the equations is proved in detail. The additive operator splitting （AOS） algorithm for the proposed model is also given. Finally, we show some numeric experimental results on images.
基金Supported by the National Natural Science Foundation of China (11171340)
文摘In this paper, we study a free boundary value problem for two-phase liquid- gas model with mass-dependent viscosity coefficient when both the initial liquid and gas masses connect to vacuum continuously. The gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid. We give the proof of the global existence and uniqueness of weak solutions whenβ∈ （0, 1）, which have improved the result of Evje and Karlsen, and we obtain the regularity of the solutions by energy method.
基金The National Natural Science Foundation of China(1116102711262009+5 种基金11226132)the Natural Science Foundation of Gansu Province(1308RJZA113)the Scientific Research Projects in Colleges and Universities of Gansu Province(2013A-043)the Fundamental Research Funds for the Gansu Universities(212084213061)the Youth Science Foundation of Lanzhou Jiaotong University(2012019)
