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On the global well‐posedness for the 2D incompressible Keller‐Segel‐Navier‐Stokes equations
Author(s) -
Zhang Qian,
Zhang Yehua
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900024
Subject(s) - uniqueness , compressibility , navier–stokes equations , mathematics , mathematical analysis , non dimensionalization and scaling of the navier–stokes equations , fourier transform , class (philosophy) , physics , computer science , mechanics , artificial intelligence
The Keller‐Segel‐Navier‐Stokes systemρ t + u · ∇ ρ = Δ ρ − ∇ · ( ρ ∇ c ) − ρ 2 ,c t + u · ∇ c = Δ c − c + ρ ,u t + u · ∇ u + ∇ P = Δ u − ρ ∇ ϕ ,∇ · u = 0 ,is considered in R 2 . It is proved that we obtain the existence and uniqueness of weak solutions for the two dimensional incompressible Keller‐Segel‐Navier‐Stokes equations for a large class of initial data by using Fourier localization technique.