$logo$

global navigaion menu / 글로벌 네비게이션 메뉴

On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics

2014.07.24 17:14

실적년도	2014년
논문구분	국외
총저자	Dongho Chae, Jihoon Lee
학술지명	Journal of Differential Equations
권(Vol.)	256
호(No.)	11
게재년월	2014년 6월
Impact Factor
SCI 등재	SCI
비고

In this paper, we establish an optimal blow-up criterion for classical solutions to the incompressible resistive Hall-magnetohydrodynamic equations. We also prove two global-in-time existence results of the classical solutions for small initial data, the smallness conditions of which are given by the suitable Sobolev and the Besov norms respectively. Although the Sobolev space version is already an improvement of the corresponding result in (4), the optimality in terms of the scaling property is achieved via the Besov space estimate. The special property of the energy estimate in terms of B 2,1s norm is essential for this result. Contrary to the usual MHD the global well-posedness in the 212 dimensional Hall-MHD is wide open.

JDE14.pdf [File Size:426.1KB/Download:73]

이 게시물을

실적년도	총저자	제목	학술지명
2014년	Youngwoo Koh, Sanghyuk Lee, Ryo Takada	Dispersive estimates for the navier-stokes equations in the rotational framework $file$	Advances in Differential Equations
2014년	Lee, Jihoon	Scaling invariant blow-up criteria for simplified versions of ericksen-leslie system $file$	Discrete and Continuous Dynamical Systems series S
2014년	Kyung-Youn Kim, Panki Kim	Two-sided estimates for the transition densities of symmetric Markov processes dominated by stable-like processes in $C^{1,\eta}$ open set $file$	Stochastic Processes and their Applications
2014년	Kil-Chan Ha, Seung-Hyeok Kye	Multi-partite separable states with unique decompositions and construction of three qubit entanglement with positive partial transpose $file$	Journal of Physics A: Mathematical and Theoretical
2014년	Kil-Chan Ha, Seung-Hyeok Kye	Global geometric difference between separable and Positive partial transpose states $file$	Open Systems & Information Dynamics
2013년	Seung-Hyeok Kye	Faces for two qubit separable states and the convex hulls of trigonometric moment curves $file$	Probability and Mathematical Statistics
2014년	Ra´ul E. Curto, In Sung Hwang and Woo Young Lee	Hyponormality of bounded-type Toeplitz operators $file$	Math. Nach.
2014년	Ra´ul E. Curto, In Sung Hwang, Dong-O Kang and Woo Young Lee	Subnormal and quasinormal Toeplitz operators with matrix-valued rational symbols $file$	Advances Mathematics
2014년	Sang Hoon Lee, Woo Young Lee, Jasang Yoon	The mean transform of bounded linear operators $file$	Journal of Mathematical Analysis and Applications
2014년	Dongho Chae	On the transport equations with singular/regular nonlocal velocities $file$	SIAM Journal on Mathematical Analysis
2014년	Dongho Chae, Tai-Peng Tsai	On discretely self-similar solutions of the euler equations $file$	Mathematical Research Letters
2014년	Dongho Chae	Euler’s equations and the maximum principle $file$	Mathematische Annalen
2014년	Dongho Chae, Peter Constantin, Jiahong Wu	An Incompressible 2D Didactic Model with Singularity and Explicit Solutions of the 2D Boussinesq Equations $file$	Journal of Mathematical Fluid Mechanics
2014년	Dongho Chae, Jihoon Lee	On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics $file$	Journal of Differential Equations
2014년	Dongho Chae	Liouville-Type Theorems for the Forced Euler Equations and the Navier-Stokes Equations $file$	Communications in Mathematical Physics
2014년	Dongho Chae	Localized energy equalities for the Navier-Stokes and the Euler equations $file$	Advances in Mathematics
2014년	고응일, 정성은, 이지은	Properties of complex symmetric operators $file$	Operators and Matrices
2014년	고응일, 정성은, 김연하, 이지은	Complex symmetric weighted composition operators on $H^2({\Bbb D})$ $file$	Journal of Functional Analysis
2013년	Sun-Sig Byun, Dian Palagachev	Boundedness of the Weak Solutions to Quasilinear Elliptic Equations with Morrey Data $file$	Indiana University Mathematics Journal
2014년	Zhen-Qing Chen, Panki Kim, Renming Song	Dirichlet Heat Kernel Estimates for Rotationally Symmetric Lévy processes $file$	Proceedings of the London Mathematical Society