caa a22 4500 60551528X CHVBK 20210128100708.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s00205-014-0802-5 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0802-5 Koba Hajime Department of Mathematics, Waseda University, 3-4-1, Okubo, Shinjuku-ku, 169-8555, Tokyo, Japan aut On Stability of the Spatially Inhomogeneous Navier-Stokes-Boussinesq System with General Nonlinearity [Elektronische Daten] [Hajime Koba] This paper considers L 2-asymptotic stability of the spatially inhomogeneous Navier-Stokes-Boussinesq system with general nonlinearity including both power nonlinear terms and convective terms. We construct a local-in-time strong solution of the system by applying semigroup theory on Hilbert spaces and fractional powers of the Stokes-Laplace operator. It is also shown that under some assumptions on an energy inequality the system has a unique global-in-time strong solution when the initial datum is sufficiently small. Furthermore, we investigate the asymptotic stability of the global-in-time strong solution by using an energy inequality, maximal L p -in-time regularity for Hilbert space-valued functions, and fractional powers of linear operators in a solenoidal L 2-space. We introduce new methods for showing the asymptotic stability by applying an energy inequality and maximal L p -in-time regularity for Hilbert space-valued functions. Our approach in this paper can be applied to show the asymptotic stability of energy solutions for various incompressible viscous fluid systems and the stability of small stationary solutions whose structure is not clear. Springer-Verlag Berlin Heidelberg, 2014 Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/3(2015-03-01), 907-965 0003-9527 215:3<907 2015 215 205 https://doi.org/10.1007/s00205-014-0802-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0802-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Koba Hajime Department of Mathematics, Waseda University, 3-4-1, Okubo, Shinjuku-ku, 169-8555, Tokyo, Japan aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/3(2015-03-01), 907-965 0003-9527 215:3<907 2015 215 205