This article considers the global regularity to the initial-boundary value problem for the 2D incompressible MHD with mixed partial dissipation and magnetic diffusion. To overcome the difficulty caused by the vanishin...This article considers the global regularity to the initial-boundary value problem for the 2D incompressible MHD with mixed partial dissipation and magnetic diffusion. To overcome the difficulty caused by the vanishing viscosities, we first establish the elliptic system for ux and by, which are estimated by 7 × us and × by, respectively. Then, we establish the global estimates for × u and ×b.展开更多
For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the globa...For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the global existence of H 2 classical solution to the Cauchy problem with small initial data is obtained.展开更多
基金supported by the Scientific Research Funds of Huaqiao University(14BS309)the National Natural Science Foundation of China(11526091)
文摘This article considers the global regularity to the initial-boundary value problem for the 2D incompressible MHD with mixed partial dissipation and magnetic diffusion. To overcome the difficulty caused by the vanishing viscosities, we first establish the elliptic system for ux and by, which are estimated by 7 × us and × by, respectively. Then, we establish the global estimates for × u and ×b.
基金Supported by the NSF of China(t0571024)Supported by the NSF of Henan Province(200511051700)Supported by the NSF of Educational Department of Henan Province(200510078005)
基金supported by the Fudan University Creative Student Cultivation Program in Key Disciplinary Areas (No. EHH1411208)
文摘For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the global existence of H 2 classical solution to the Cauchy problem with small initial data is obtained.
