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Global large solutions of the Cauchy problem for the NS-NPP equations with Fujita-Kato type initial data
Abstract
In this paper, we prove the global well-posedness of the Cauchy problem for the NS-NPP equations with some large Fujita-Kato type initial data. Specifically, we show that there exist two positive constants c0 and C0 such that if the initial data (u0, N0, P0) satisfies the following condition: (|u0|Ḣ−1+d/2+|N0−P0|Ḣ−2+d/2)exp{C0(|N0+P0|Ḣ−2+d/22+1)} ≤ c0, then the NS-NPP equations admits a unique global solution. This result implies global existence of solutions without any smallness conditions imposed on the sum of initial particle densities of negative and positive electric charge in the framework of Sobolev spaces.
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BibTeX
@misc{zhao2026global,
title = {{Global large solutions of the Cauchy problem for the NS-NPP equations with Fujita-Kato type initial data}},
author = {Jihong Zhao and Chao Deng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08533},
eprint = {2609.08533},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08533},
}
RIS
TY - UNPB
TI - Global large solutions of the Cauchy problem for the NS-NPP equations with Fujita-Kato type initial data
AU - Jihong Zhao
AU - Chao Deng
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08533
UR - https://arxiv.org/abs/2609.08533
AB - In this paper, we prove the global well-posedness of the Cauchy problem for the NS-NPP equations with some large Fujita-Kato type initial data. Specifically, we show that there exist two positive constants c_0 and C_0 such that if the initial data (u_0, N_0, P_0) satisfies the following condition: (|u_0|_Ḣ^−1+d/2+|N_0−P_0|_Ḣ^−2+d/2)exp{C_0(|N_0+P_0|_Ḣ^−2+d/2^2+1)} ≤ c_0, then the NS-NPP equations admits a unique global solution. This result implies global existence of solutions without any smallness conditions imposed on the sum of initial particle densities of negative and positive electric charge in the framework of Sobolev spaces.
ER -