Global existence and time decay rates for the 3D bipolar compressible Navier-Stokes-Poisson system with unequal viscosities

We consider the Cauchy problem for the three-dimensional bipolar compressible Navier-Stokes-Poisson system with unequal viscosities. Under the assumption that the H 3 norm of the initial data is small but its higher order derivatives can be arbitrarily large, the global existence and uniqueness of s...

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Bibliographic Details
Published in:Science China. Mathematics 2022-04, Vol.65 (4), p.731-752
Main Authors: Wu, Guochun, Zhang, Yinghui, Zhang, Anzhen
Format: Article
Language:English
Subjects:
Applications of Mathematics
Cauchy problems
Compressibility
Decay rate
Energy methods
Fluid flow
Interpolation
Mathematics
Mathematics and Statistics
Navier-Stokes equations
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Summary:We consider the Cauchy problem for the three-dimensional bipolar compressible Navier-Stokes-Poisson system with unequal viscosities. Under the assumption that the H 3 norm of the initial data is small but its higher order derivatives can be arbitrarily large, the global existence and uniqueness of smooth solutions are obtained by an ingenious energy method. Moreover, if additionally, the H ˙ − s ( 1 2 ⩽ s < 3 2 ) or B ˙ 2 , ∞ − s ( 1 2 < s ⩽ 3 2 ) norm of the initial data is small, the optimal decay rates of solutions are also established by a regularity interpolation trick and delicate energy methods.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-020-1719-9