We consider a Keller–Segel model coupled to the incompressible Navier–Stokes system in 3-dimensional case.We prove that the system has a unique local solution when(u0,n0,c0)∈Φ_(01)^(1)×Φ_(01)^(2)×Φ_(01...We consider a Keller–Segel model coupled to the incompressible Navier–Stokes system in 3-dimensional case.We prove that the system has a unique local solution when(u0,n0,c0)∈Φ_(01)^(1)×Φ_(01)^(2)×Φ_(01)^(3),where Φ_(01)^(1)×Φ_(01)^(2)×Φ_(01)^(3) is a subspace of bmo^(−1)(R^(3))×B˙_(p,∞)^(−2+3/p) (R^(3))×(B˙_(q,∞)^(3/q) (R^(3))∩L^(∞)(R^(3))).Furthermore,we obtain that the system exists a unique global solution for any small initial data(u0,n0,c0)∈BMO^(−1)(R^(3))×B˙_(p,∞)^(−2+3/p)(R^(3))×(B_(q,∞)^(3/q)(R^(3))∩L^(∞)(R^(3))).For the difference between these spaces and known ones,our results may be regarded as a new existence theorem on the system.展开更多
基金Supported by NSFC(Grant Nos.12161041 and 12071197)Training Program for academic and technical leaders of major disciplines in Jiangxi Province(Grant No.20204BCJL23057)Natural Science Foundation of Jiangxi Province(Grant No.20212BAB201008)。
文摘We consider a Keller–Segel model coupled to the incompressible Navier–Stokes system in 3-dimensional case.We prove that the system has a unique local solution when(u0,n0,c0)∈Φ_(01)^(1)×Φ_(01)^(2)×Φ_(01)^(3),where Φ_(01)^(1)×Φ_(01)^(2)×Φ_(01)^(3) is a subspace of bmo^(−1)(R^(3))×B˙_(p,∞)^(−2+3/p) (R^(3))×(B˙_(q,∞)^(3/q) (R^(3))∩L^(∞)(R^(3))).Furthermore,we obtain that the system exists a unique global solution for any small initial data(u0,n0,c0)∈BMO^(−1)(R^(3))×B˙_(p,∞)^(−2+3/p)(R^(3))×(B_(q,∞)^(3/q)(R^(3))∩L^(∞)(R^(3))).For the difference between these spaces and known ones,our results may be regarded as a new existence theorem on the system.
