Pointwise Estimates for Bipolar Compressible Navier–Stokes–Poisson System in Dimension Three

Pointwise Estimates for Bipolar Compressible Navier–Stokes–Poisson System in Dimension Three The Cauchy problem of the bipolar Navier–Stokes–Poisson system (1.1) in dimension three is considered. We obtain the pointwise estimates of the time-asymptotic shape of the solution, which exhibit a generalized Huygens’ principle as the Navier–Stokes system. This phenomenon is the most important difference from the unipolar Navier–Stokes–Poisson system. Due to the non-conservative structure of the system (1.1) and the interplay of two carriers which counteract the influence of the electric field (a nonlocal term), some new observations are essential for the proof. We fully use the conservative structure of the system for the total density and total momentum, and the mechanism of the linearized unipolar Navier–Stokes–Poisson system together with the special form of the nonlinear terms in the system for the difference of densities and the difference of momentums. Lastly, as a byproduct, we extend the usual $${L^2({\mathbb{R}}^3)}$$ L 2 ( R 3 ) -decay rate to the $${L^p({\mathbb{R}}^3)}$$ L p ( R 3 ) -decay rate with $${p > 1}$$ p > 1 and also improve former decay rates. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Rational Mechanics and Analysis Springer Journals

Pointwise Estimates for Bipolar Compressible Navier–Stokes–Poisson System in Dimension Three

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag GmbH Germany
Subject
Physics; Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics
ISSN
0003-9527
eISSN
1432-0673
D.O.I.
10.1007/s00205-017-1140-1
Publisher site
See Article on Publisher Site

Abstract

The Cauchy problem of the bipolar Navier–Stokes–Poisson system (1.1) in dimension three is considered. We obtain the pointwise estimates of the time-asymptotic shape of the solution, which exhibit a generalized Huygens’ principle as the Navier–Stokes system. This phenomenon is the most important difference from the unipolar Navier–Stokes–Poisson system. Due to the non-conservative structure of the system (1.1) and the interplay of two carriers which counteract the influence of the electric field (a nonlocal term), some new observations are essential for the proof. We fully use the conservative structure of the system for the total density and total momentum, and the mechanism of the linearized unipolar Navier–Stokes–Poisson system together with the special form of the nonlinear terms in the system for the difference of densities and the difference of momentums. Lastly, as a byproduct, we extend the usual $${L^2({\mathbb{R}}^3)}$$ L 2 ( R 3 ) -decay rate to the $${L^p({\mathbb{R}}^3)}$$ L p ( R 3 ) -decay rate with $${p > 1}$$ p > 1 and also improve former decay rates.

Journal

Archive for Rational Mechanics and AnalysisSpringer Journals

Published: Jun 10, 2017

References

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