Publication Date:
2021-04-16
Description:
In this paper, we consider the linear stability of blowup solution for incompressible Keller–Segel–Navier–Stokes system in whole space $mathbb{R}^{3}$ R 3 . More precisely, we show that, if the initial data of the three dimensional Keller–Segel–Navier–Stokes system is close to the smooth initial function $(0,0,extbf{u}_{s}(0,x) )^{T}$ ( 0 , 0 , u s ( 0 , x ) ) T , then there exists a blowup solution of the three dimensional linear Keller–Segel–Navier–Stokes system satisfying the decomposition $$ igl(n(t,x),c(t,x),extbf{u}(t,x) igr)^{T}= igl(0,0, extbf{u}_{s}(t,x) igr)^{T}+mathcal{O}(varepsilon ), quad forall (t,x)in igl(0,T^{*} igr) imes mathbb{R}^{3}, $$ ( n ( t , x ) , c ( t , x ) , u ( t , x ) ) T = ( 0 , 0 , u s ( t , x ) ) T + O ( ε ) , ∀ ( t , x ) ∈ ( 0 , T ∗ ) × R 3 , in Sobolev space $H^{s}(mathbb{R}^{3})$ H s ( R 3 ) with $s=frac{3}{2}-5a$ s = 3 2 − 5 a and constant $0〈 all 1$ 0
Print ISSN:
1687-2762
Electronic ISSN:
1687-2770
Topics:
Mathematics
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