Related papers: Global large solution for the tropical climate mod…
We consider dimensional crossover for an O(N) model on a d-dimensional layered geometry of thickness L, in the sigma-model limit, using ``environmentally friendly'' renormalization. We show how to derive critical temperature shifts, giving…
As a tool for understanding the meridional circulation of the atmosphere, a two-dimensional ( latitude -- height ) numerical model is used to clarify the relationship between the Hadley circulation and large-scale motions associated with…
In this paper, we consider a linear heat equation with constant coefficients and a single constant delay. Such equations are commonly used to model and study various problems arising in ecology and population biology when describing the…
We calculate the thermal diffusivity $D = \kappa/c_{\rho}$ and butterfly velocity $v_B$ in holographic models that flow to AdS$_2 \times R^{d}$ fixed points in the infra-red. We show that both these quantities are governed by the same…
Motivated by \cite{CG10,CZ6}, we prove the global existence of solutions to the two-dimensional isentropic compressible Navier-Stokes equations with smooth initial data which are slowly varying in one direction and with initial density…
In this paper, we study the global well-posedness and optimal time decay rates of strong solutions to the diffusion approximation model in radiation hydrodynamics in $\mathbb{R}^3$. This model consists of the full compressible Navier-Stokes…
This work examines the global dynamics of classical solutions of a two-stage (juvenile-adult) reaction-diffusion population model in time-periodic and spatially heterogeneous environments. It is shown that the sign of the principal…
Large ensembles of climate projections are essential for characterizing uncertainty in future climate and extreme weather events, yet computational constraints of numerical climate models limit ensemble sizes to a small number of…
A large fraction of known terrestrial-size exoplanets located in the Habitable Zone of M-dwarfs are expected to be tidally-locked. Numerous efforts have been conducted to study the climate of such planets, using in particular 3-D Global…
We first construct the global unique solution by assuming that the initial data is small in the $H^3$ norm but the higher order derivatives could be large. If further the initial data belongs to $\Dot{H}^{-s}$ ($0\le s<3/2$) or…
We consider the thermal behavior of a large number of matrix degrees of freedom in the planar limit. We work in $0+1$ dimensions, with $D$ matrices, and use $1/D$ as an expansion parameter. This can be thought of as a non-commutative…
In this paper, we investigate the optimal large-time behavior of the global solution to a singular chemotaxis system in the whole space $\mathbb{R}^d$ with $d=2,3$. Assuming that the initial data is sufficiently close to an equilibrium…
The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a…
In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a…
In this paper, we study large time asymptotic behavior of the elastic displacement $u$ and the temperature difference $\theta$ for the thermoelastic systems of type II and type III in the whole space $\mathbb{R}^n$ without using the thermal…
Tropical cyclones are known to expand to an equilibrium size on the $f$-plane, but the expansion process is not understood. In this study, an analytical model for tropical cyclone size expansion on the $f$-plane is proposed. Conceptually,…
Observing the special structure of the system and using the Poincar{\'{e}}-Sobolev inequality, we establish Liouville type theorems for the 3D steady tropical climate model under certain conditions on $u$, $v$, $\nabla \theta$. Our results…
We prove existence and uniqueness of smooth solutions with large initial data for a system of equations modeling the interaction of short waves, governed by a nonlinear Schr\"odinger equation, and long waves, described by the equations of…
This work is devoted to the study of a viscous shallow-water system with friction and capillarity term. We prove in this paper the existence of global strong solutions for this system with some choice of large initial data when $N\geq 2$ in…
This paper is concerned with the two-dimensional chemotaxis-fluid model \begin{equation*} \begin{cases} n_t+u\cdot\nabla n=\Delta (n\phi(v))+\mu n(1-n),\\ v_t+u\cdot\nabla v=\Delta v-nv,\\ u_t+ \kappa (u\cdot\nabla) u=\Delta…