Optimal decay rate for higher–order derivatives of solution to the 3D compressible quantum magnetohydrodynamic model
| Autor: | Wang Juan, Zhang Yinghui |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Advances in Nonlinear Analysis, Vol 11, Iss 1, Pp 830-849 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2191-9496 2191-950X |
| DOI: | 10.1515/anona-2021-0219 |
| Popis: | We investigate optimal decay rates for higher–order spatial derivatives of strong solutions to the 3D Cauchy problem of the compressible viscous quantum magnetohydrodynamic model in the H5 × H4 × H4 framework, and the main novelty of this work is three–fold: First, we show that fourth order spatial derivative of the solution converges to zero at the L2-rate (1+t)-114{L^2} - {\rm{rate}}\,{(1 + t)^{- {{11} \over 4}}} , which is same as one of the heat equation, and particularly faster than the L2-rate (1+t)-54{L^2} - {\rm{rate}}\,{(1 + t)^{- {5 \over 4}}} in Pu–Xu [Z. Angew. Math. Phys., 68:1, 2017] and the L2-rate (1+t)-94{L^2} - {\rm{rate}}\,{(1 + t)^{- {9 \over 4}}} , in Xi–Pu–Guo [Z. Angew. Math. Phys., 70:1, 2019]. Second, we prove that fifth–order spatial derivative of density ρ converges to zero at the L2-rate (1+t)-134{L^2} - {\rm{rate}}\,{(1 + t)^{- {{13} \over 4}}} , which is same as that of the heat equation, and particularly faster than ones of Pu–Xu [Z. Angew. Math. Phys., 68:1, 2017] and Xi–Pu–Guo [Z. Angew. Math. Phys., 70:1, 2019]. Third, we show that the high-frequency part of the fourth order spatial derivatives of the velocity u and magnetic B converge to zero at the L2-rate (1+t)-134{L^2} - {\rm{rate}}\,{(1 + t)^{- {{13} \over 4}}} , which are faster than ones of themselves, and totally new as compared to Pu–Xu [Z. Angew. Math. Phys., 68:1, 2017] and Xi–Pu–Guo [Z. Angew. Math. Phys., 70:1, 2019]. |
| Databáze: | Directory of Open Access Journals |
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