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Lower bound of decay rate for higher order derivatives of solution to the compressible quantum magnetohydrodynamic model
Author(s) -
Gao Jincheng,
Lyu Zeyu,
Yao Zhengan
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6974
Subject(s) - upper and lower bounds , mathematics , compressibility , norm (philosophy) , magnetohydrodynamic drive , order (exchange) , constant (computer programming) , bound state , time derivative , mathematical analysis , physics , mathematical physics , magnetohydrodynamics , quantum mechanics , magnetic field , thermodynamics , finance , political science , computer science , law , economics , programming language
The lower bounds of decay rates for global solution to the compressible viscous quantum magnetohydrodynamic model in three‐dimensional whole space under the H 5 × H 4 × H 4 framework are investigated in this paper. We first show that the lower bound of decay rate for the solution converging to constant equilibrium state (1, 0, 0) in L 2 ‐norm is( 1 + t ) − 3 4when the initial data satisfy some low‐frequency assumption. Moreover, we prove that the lower bound of decay rate of k ( k ∈ [1, 3]) order spatial derivative for the solution converging to constant equilibrium state (1, 0, 0) in L 2 ‐norm is( 1 + t ) − 3 + 2 k 4. Then, we show that the lower bound of decay rate for the time derivatives of density and velocity is( 1 + t ) − 5 4, but the lower bound of decay rate for the time derivative of magnetic field converging to zero in L 2 ‐norm is( 1 + t ) − 7 4.