This article studies the initial-boundary value problem for a three dimensional magnetic-curvature-driven Rayleigh-Taylor model. We first obtain the global existence of weak solutions for the full model equation by employing the Galerkin's approximation method. Secondly, for a slightly simplified model, we show the existence and uniqueness of global strong solutions via the Banach's fixed point theorem and vanishing viscosity method.
Xueke PU
,
Boling GUO
. INITIAL BOUNDARY VALUE PROBLEM FOR THE 3D MAGNETIC-CURVATURE-DRIVEN RAYLEIGH-TAYLOR MODEL[J]. Acta mathematica scientia, Series B, 2020
, 40(2)
: 529
-542
.
DOI: 10.1007/s10473-020-0215-5
[1] Das A, Sen A, Kaw P. Nonlinear saturated states of the magnetic-curvature-driven Rayleigh-Taylor instability in three dimensions. Phys Plasma, 2005, 12:022302
[2] Guo B, Han Y. Existence and uniqueness of global solution of the Hasegawa-Mima equation. J Math Phys, 2004, 45:1638-1647
[3] Hasegawa A, Mima K. Stationary spectrum of strong turbulence in magnetized plasma. Phys Rev Lett, 1977, 39:205-208
[4] Hasegawa A, Mima K. Pesudo-three-dimensional turbulence in magnetized nonuniform plasma. Phys Fluids, 1978, 21:87-92
[5] Hasegawa A, Wakatani M. Plasma edge turbulence. Phys Rev Lett, 1983, 50:682-686
[6] Hasegawa A, Wakatani M. A collisional drift wave description of plasma edge turbulence. Phys Fluids, 1984, 27:611-618
[7] Kato T. Nonstationary flows of viscous and ideal fluids in R3. J Funct Anal, 1972, 9:296-305
[8] Ladyzhenskaya O A, Solonnikov V A, Ural'ceva N N. Linear and quasi-linear equations of parabolic type. Providence:Amer Math Soc, 1968
[9] Lions J L, Magenes E. Non-Homogeneous Boundary Value Problems and Applications, I. Berlin:SpringerVerlag, 1972
[10] Lions J L. Quelques methodes de resolution des problemes aux limits non lineeaires. Paris:Dunod, 1969
[11] Kondo A, Tani A. Initial boundary value problem for model equations of resistive drift wave turbulence. SIAM J Math Anal, 2011, 43(2):925-943
[12] Zhang R, Guo B. Global attractor for Hasegawa-Mima equation. Appl Math Mech (Engl Ed), 2006, 27:567-574
[13] Zhang R, Guo B. Dynamical behavior for the three-dimensional generalized Hasegawa-Mima equations. J Math Phys, 2007, 27:012703
