Global solutions to the Cauchy problem of BNSP equations in some classes of large data

Jie Qi; Weike Wang; Jie Qi; Weike Wang

doi:10.3934/era.2024255

Electronic Research Archive

2024, Volume 32, Issue 9: 5496-5541. doi: 10.3934/era.2024255

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Research article

Global solutions to the Cauchy problem of BNSP equations in some classes of large data

Jie Qi ^{1
,
,},
Weike Wang ^1,2

1.
School of Mathematical Sciences, CMA-Shanghai, Shanghai Jiao Tong University, Shanghai 200240, China
2.
Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China

Received: 25 June 2024 Revised: 05 September 2024 Accepted: 12 September 2024 Published: 26 September 2024

In this paper, we obtained the global existence and large time behavior of the solution for bipolar Navier-Stokes-Poisson equations under the partially smallness assumption of the initial data. Due to the complexity of bipolar Navier-Stokes-Poisson equations, we chose Green's function method instead of the classical energy method and thus discussed the regularity criterion under decaying structures in time instead of only integrability of time variable. It made the whole proof more simple and clear, meanwhile, resulted in the large time decaying estimates of the solution. It also showed the advantage of Green's function method in the study of global existence in the large perturbation framework.
- regularity criterion,
- bootstrap argument,
- Green's function,
- global existence,
- decay rate of solution
Citation: Jie Qi, Weike Wang. Global solutions to the Cauchy problem of BNSP equations in some classes of large data[J]. Electronic Research Archive, 2024, 32(9): 5496-5541. doi: 10.3934/era.2024255

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Abstract

In this paper, we obtained the global existence and large time behavior of the solution for bipolar Navier-Stokes-Poisson equations under the partially smallness assumption of the initial data. Due to the complexity of bipolar Navier-Stokes-Poisson equations, we chose Green's function method instead of the classical energy method and thus discussed the regularity criterion under decaying structures in time instead of only integrability of time variable. It made the whole proof more simple and clear, meanwhile, resulted in the large time decaying estimates of the solution. It also showed the advantage of Green's function method in the study of global existence in the large perturbation framework.

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