首页|Space-time estimates of the 3D bipolar compressible Navier-Stokes-Poisson system with unequal viscosities

Space-time estimates of the 3D bipolar compressible Navier-Stokes-Poisson system with unequal viscosities

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The space-time behavior for the Cauchy problem of the 3D compressible bipolar Navier-Stokes-Poisson(BNSP)system with unequal viscosities is given.The space-time estimate of the electric field▽ø=▽(-△)-1(n-Zρ)is the most important in deducing generalized Huygens'principle for the BNSP system and it requires proving that the space-time estimate of n-Zρ only contains the diffusion wave due to the singularity of the operator ▽(-△)-1.A suitable linear combination of unknowns reformulating the original system into two small subsystems for the special case(with equal viscosities)in Wu and Wang(2017)is crucial for both linear analysis and nonlinear estimates,especially for the space-time estimate of ▽φ.However,the benefits from this reformulation will no longer exist in general cases.Here,we study an 8 x 8 Green's matrix directly.More importantly,each entry in Green's matrix contains wave operators in the low-frequency part,which will generally produce Huygens'wave;as a result,one cannot achieve the space-time estimate of n-Zρthat only contains the diffusion wave as before.We overcome this difficulty by taking a more detailed spectral analysis and developing new estimates arising from subtle cancellations in Green's function.

Green's functionbipolar Navier-Stokes-Poisson systemunequal viscosities

Zhigang Wu、Weike Wang

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Department of Mathematics,Donghua University,Shanghai 201620,China

School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China

Shanghai Frontier Science Center of Modern Analysis(CMA-Shanghai),Shanghai Jiao Tong University,Shanghai 200240,China

National Natural Science Foundation of ChinaNatural Science Foundation of ShanghaiNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaShanghai Science and Technology Innovation Action Plan

1197110022ZR140230012271357121611410041183101121JC1403600

2024

10.1007/s11425-022-2130-2

中国科学:数学(英文版)
中国科学院

中国科学:数学(英文版)

CSTPCD
影响因子：0.36
ISSN：1674-7283
年,卷(期)：2024.67(5)