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Periodic solutions for Boussinesq systems in weak-Morrey spaces | | Pham Truong Xuan
; Nguyen Thi Van
; Tran Van Thuy
; | | Date: |
1 Sep 2023 | | Abstract: | We prove the existence and polynomial stability of periodic mild solutions
for Boussinesq systems in critical weak-Morrey spaces for dimension
$ngeqslant3$. Those systems are derived via the Boussinesq approximation and
describe the movement of an incompressible viscous fluid under natural
convection filling the whole space $mathbb{R}^{n}$. Using certain dispersive
and smoothing properties of heat semigroups on Morrey-Lorentz spaces as well as
Yamazaki-type estimate on block spaces, we prove the existence of bounded mild
solutions for the linear equations corresponding to the Boussinesq system.
Then, we establish a Massera-type theorem to obtain the existence and
uniqueness of periodic solutions to corresponding linear equations on the
half-line by using a mean-ergodic method. Next, using fixed point arguments, we
can pass from linear equations to prove the existence uniqueness and polynomial
stability of such solutions for Boussinesq systems. Finally, we apply the
results to Navier-Stokes equations. | | Source: | arXiv, 2309.00191 | | Services: | Forum | Review | PDF | Favorites | |
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