In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role fo...In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role for 2-dimensional setting in the constructive proof of the fact that the spaces of polynomial splines with smoothness rand total degree k≥3r+2 over arbitrary triangulations achieve the optimal approximation order with the approximation constant depending only on k and the smallest angle of the partition in [5].展开更多
In this paper, we consider the viscous incompressible magnetohydrodynamic （MHD） system with a new boundary condition for a general smooth domain in R^3. We obtain the well-posedness of the system and the vanishing v...In this paper, we consider the viscous incompressible magnetohydrodynamic （MHD） system with a new boundary condition for a general smooth domain in R^3. We obtain the well-posedness of the system and the vanishing viscosity limit result.展开更多
文摘In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role for 2-dimensional setting in the constructive proof of the fact that the spaces of polynomial splines with smoothness rand total degree k≥3r+2 over arbitrary triangulations achieve the optimal approximation order with the approximation constant depending only on k and the smallest angle of the partition in [5].
基金The authors were partially supported by the National Natural Science Foundation of China （No.11371042）.
文摘In this paper, we consider the viscous incompressible magnetohydrodynamic （MHD） system with a new boundary condition for a general smooth domain in R^3. We obtain the well-posedness of the system and the vanishing viscosity limit result.
