Related papers: Global regularity for a class of 3D tropical clima…
In this paper, we establish the global well-posedness of stochastic 3D Leray-$\alpha$ model with general fractional dissipation driven by multiplicative noise. This model is the stochastic 3D Navier-Stokes equation regularized through a…
There is argument as to the extent to which there has been an increase over the past few decades in the frequency of the extremes of climatic parameters, such as temperature, storminess, precipitation, etc, an obvious point being that…
We present a large ensemble of simulations of an Earth-like world with increasing insolation and rotation rate. Unlike previous work utilizing idealized aquaplanet configurations we focus our simulations on modern Earth-like topography. The…
We study a nonlinear parabolic system for a time dependent solenoidal vector field on $\Bbb R^3$. The nonlinear term of this new model equations is obtained slightly modifying that of the Navier-Stokes equations. The system has the same…
Earth System Models (ESMs) are essential tools for understanding the impact of human actions on Earth's climate. One key application of these models is studying extreme weather events, such as heat waves or dry spells, which have…
We establish three partial differential equation models describing the thermodynamics of the fluid, by combining the energetic variational approach, appropriate constitutive relations, and classical thermodynamics laws. What is more, by…
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 present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially…
We consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a…
It is well known, by now, that the three-dimensional non-viscous planetary geostrophic model, with vertical hydrostatic balance and horizontal Rayleigh friction, coupled to the heat diffusion and transport, is mathematically ill-posed. This…
In this article we study the global regularity of 2D generalized magnetohydrodynamic equations (2D GMHD), in which the dissipation terms are $- \nu (- \triangle)^{\alpha} u$ and $- \kappa (-\triangle)^{\beta} b$. We show that smooth…
In this paper we study a fractional diffusion Boussinesq model which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion for the temperature. We prove global well-posedness results.
Convective processes are crucial in shaping exoplanetary atmospheres but are computationally expensive to simulate directly. A novel technique of simulating moist convection on tidally locked exoplanets is to use a global 3D model with a…
We introduce a fractional order SIRS model with non-linear incidence rate. Existence of a unique positive solution to the model is proved. Stability analysis of the disease free equilibrium and positive fixed points are investigated.…
We solve here the so called division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that semilinear wave equations which can be written as systems involving quadratic derivative…
This note is focused on a novel technique in order to establish the boundedness in more regular spaces for global attractors of dissipative dynamical systems, without appealing to uniform-in-time estimates. As an application of the abstract…
We analyze how climate change affects marine oxygen production by modeling plankton--oxygen dynamics with a fractional-order nonlinear system and establishing rigorous conditions for the model's well-posedness. We formulate a…
Earth's modern climate is characterized by wet, rainy deep tropics, however paleoclimate and planetary science have revealed a wide range of hydrological cycle regimes connected to different external parameters. Here we investigate how…
Climate change is a reality of today. Paleoclimatic proxies and climate predictions based on coupled atmosphere-ocean general circulation models provide us with temperature data. Using Detrended Fluctuation Analysis, we are investigating…
In this paper, we discuss with the global well-posedness of 2D anisotropic nonlinear Boussinesq equations with any two positive viscosities and one positive thermal diffusivity. More precisely, for three kinds of viscous combinations, we…