caa a22 4500 606194231 CHVBK 20210128100913.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00030-014-0309-7 doi (NATIONALLICENCE)springer-10.1007/s00030-014-0309-7 On the global well-posedness of a generalized 2D Boussinesq equations [Elektronische Daten] [Junxiong Jia, Jigen Peng, Kexue Li] In this paper, we consider the global solutions to a generalized 2D Boussinesq equation $$\left \{ \begin{array}{ll}\partial_{t} \omega + u \cdot \nabla \omega + \nu \Lambda^{\alpha} \omega = \theta_{x_{1}} , \quad \\ u = \nabla^{\bot} \psi = (-\partial_{x_{2}} , \partial_{x_{1}}) \psi , \quad \Delta \psi = \Lambda^{\sigma} (\log (I-\Delta))^{\gamma} \omega , \quad \\ \partial_{t} \theta + u\cdot \nabla \theta + \kappa \Lambda^{\beta} \theta = 0, \quad \\ \omega(x,0) = \omega_{0}(x) , \quad \theta(x,0) = \theta_{0}(x),\end{array}\right.$$ ∂ t ω + u · ∇ ω + ν Λ α ω = θ x 1 , u = ∇ ⊥ ψ = ( - ∂ x 2 , ∂ x 1 ) ψ , Δ ψ = Λ σ ( log ( I - Δ ) ) γ ω , ∂ t θ + u · ∇ θ + κ Λ β θ = 0 , ω ( x , 0 ) = ω 0 ( x ) , θ ( x , 0 ) = θ 0 ( x ) , with $${\sigma \geq 0}$$ σ ≥ 0 , $${\gamma \geq 0}$$ γ ≥ 0 , $${\nu > 0}$$ ν > 0 , $${\kappa > 0}$$ κ > 0 , $${\alpha < 1}$$ α < 1 and $${\beta < 1}$$ β < 1 . When $${\sigma = 0}$$ σ = 0 , $${\gamma \geq 0}$$ γ ≥ 0 , $${\alpha \in [0.95,1)}$$ α ∈ [ 0.95 , 1 ) and $${\beta \in (1-\alpha,g(\alpha))}$$ β ∈ ( 1 - α , g ( α ) ) , where $${g(\alpha) < 1}$$ g ( α ) < 1 is an explicit function as a technical bound, we prove that the above equation has a global and unique solution in suitable functional space. Springer Basel, 2015 Generalized 2D Boussinesq equation nationallicence Global regularity nationallicence Supercritical Boussinesq equations nationallicence Regularization effect nationallicence Jia Junxiong Department of Mathematics, Xi'an Jiaotong University, 710049, Xi'an, China aut Peng Jigen Department of Mathematics, Xi'an Jiaotong University, 710049, Xi'an, China aut Li Kexue Department of Mathematics, Xi'an Jiaotong University, 710049, Xi'an, China aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/4(2015-08-01), 911-945 1021-9722 22:4<911 2015 22 30 https://doi.org/10.1007/s00030-014-0309-7 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/s00030-014-0309-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jia Junxiong Department of Mathematics, Xi'an Jiaotong University, 710049, Xi'an, China aut NATIONALLICENCE 700 1- Peng Jigen Department of Mathematics, Xi'an Jiaotong University, 710049, Xi'an, China aut NATIONALLICENCE 700 1- Li Kexue Department of Mathematics, Xi'an Jiaotong University, 710049, Xi'an, China aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/4(2015-08-01), 911-945 1021-9722 22:4<911 2015 22 30