SHARP DECAY ESTIMATES FOR SMALL DATA SOLUTIONS TO THE MAGNETIZED VLASOV-POISSON SYSTEM AND MAGNETIZED VLASOV-YUKAWA SYSTEM

Xianghong Hu; Xianwen Zhang

doi:10.11948/20230332

2024 Volume 14 Issue 3

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Xianghong Hu, Xianwen Zhang. SHARP DECAY ESTIMATES FOR SMALL DATA SOLUTIONS TO THE MAGNETIZED VLASOV-POISSON SYSTEM AND MAGNETIZED VLASOV-YUKAWA SYSTEM[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1648-1673. doi: 10.11948/20230332

Citation:

Xianghong Hu, Xianwen Zhang. SHARP DECAY ESTIMATES FOR SMALL DATA SOLUTIONS TO THE MAGNETIZED VLASOV-POISSON SYSTEM AND MAGNETIZED VLASOV-YUKAWA SYSTEM[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1648-1673. doi: 10.11948/20230332

SHARP DECAY ESTIMATES FOR SMALL DATA SOLUTIONS TO THE MAGNETIZED VLASOV-POISSON SYSTEM AND MAGNETIZED VLASOV-YUKAWA SYSTEM

Xianghong Hu^1,,
Xianwen Zhang^1, ,

1.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

Author Bio: Email: xianghonghu@hust.edu.cn(X. Hu)
Corresponding author: Email: xwzhang@hust.edu.cn(X. Zhang)
Fund Project: The authors were supported by National Natural Science Foundation of China (Grant No. 11871024)

Abstract

Abstract

In this article, we present sharp decay estimates for small data solutions to the magnetized Vlasov-Poisson system and the magnetized Vlasov-Yukawa system in dimension three. Our arguments are based on the modification of the vector field method developed by Smulevici [42] for the Vlasov-Poisson system and improved by Duan [17] for the Vlasov-Poisson system and the Vlasov-Yukawa system. We extend the results in [17] to the magnetized case and slightly improve the decay estimates, our method improve the result in [48], in which a similar result was obtained but the norms considered have additional v-weighted L^p-norms. In our work, we do not need the extra L^p-norms.
- Small data solution /
- magnetized Vlasov-Poisson system /
- magnetized Vlasov-Yukawa system /
- vector field method /
- decay estimate
MSC: 35B40, 35Q49, 35Q83, 82D10

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References

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