In this paper,solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary.A clas...In this paper,solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary.A class of additional boundary conditions for the vorticities are identified so that the solution is unique and stable.展开更多
The initial-Dirichlet and initial-Neumann problems in Lipschitz cylinders are studied forthe general second order parabolic equations of constant coefficients with squarely integrableboundary data. By layer potential ...The initial-Dirichlet and initial-Neumann problems in Lipschitz cylinders are studied forthe general second order parabolic equations of constant coefficients with squarely integrableboundary data. By layer potential method developed in the past decade, the author provesthat the double layer potential and the single layer potential operators are invertible and henceobtains the solvability of the initial boundsry value problems. Also, the solutions can berepresented by these operators.展开更多
基金supported by the National Natural Science Foundation of China (No.10771173)the Zheng Ge Ru Foundation,the Hong Kong RGC Earmarked Research (Nos.CUHK4028/04P,CUHK4040/06P,CUHK4042/08P)the RGC Central Allocation (No.CA05/06.SC01)
文摘In this paper,solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary.A class of additional boundary conditions for the vorticities are identified so that the solution is unique and stable.
文摘The initial-Dirichlet and initial-Neumann problems in Lipschitz cylinders are studied forthe general second order parabolic equations of constant coefficients with squarely integrableboundary data. By layer potential method developed in the past decade, the author provesthat the double layer potential and the single layer potential operators are invertible and henceobtains the solvability of the initial boundsry value problems. Also, the solutions can berepresented by these operators.
