Global well-posedness and energy decay for hypodissipative three-dimensional tropical climate models with damping
Abstract
Abstract In this paper, we consider a three-dimensional tropical climate model (TCM) with fractional diffusion Λ2αu and, in particular, nonlinear damping |u|β−1u in the equation for the barotropic mode of the velocity u. Assuming α∈(9/10,1] and exploiting the regularizing effect due to the damping term, we establish the global existence and uniqueness of strong solutions for β greater than a suitable threshold depending on α. In the given analysis, we place particular emphasis on the case of hypoviscosity. As a further result, we prove the L2-energy decay of the global solution (u,v,θ) over the long-time period.
Fields of Study & Subjects
Navier-Stokes equation solutions
Mathematical Biology Tumor Growth
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences
- Publisher
- The Royal Society
- Volume
- 482
- Issue
- 2336
- Publication date
- 15 April 2026
- Language
- EN