相关论文: Global small solutions to a tropical climate model…

In the first part of this work, we investigate the Cauchy problem for the $d$-dimensional incompressible Oldroyd-B model with dissipation in the stress tensor equation. By developing a weighted Chemin-Lerner framework combined with a…

Let $\mathbb{H}^n$ be the $n$-dimensional real hyperbolic space, $\Delta$ its nonnegative Laplace--Beltrami operator whose bottom of the spectrum we denote by $\lambda_{0}$, and $\sigma \in (0,1)$. The aim of this paper is twofold. On the…

We develop a microscopic theory of thermalisation for a thermometer coupled to a many-body bath beyond standard Markovian and Fermi-golden-rule assumptions. By modeling interaction matrix elements in the non-interacting basis as independent…

In this contribution we prove the existence of weak solutions to degenerate parabolic systems arising from the coupled moisture movement, transport of dissolved species and heat transfer through partially saturated porous materials.…

In this paper, the emergence of macroscopic-scale pseudo time-irreversibility is studied in the closed classical many-body system of pair interacting particles. First, exact continuum equations are derived to the Hamiltonian dynamics…

We introduce a simple model of the time evolution of a binary mixture of compressible fluids including the thermal effects. Despite its apparent simplicity, the model is thermodynamically consistent admitting an entropy balance equation. We…

We obtain novel closed form solutions to the Friedmann equation for cosmological models containing a component whose equation of state is that of radiation $(w=1/3)$ at early times and that of cold pressureless matter $(w=0)$ at late times.…

M. Budyko and W. Sellers independently introduced seminal energy balance climate models in 1969, each with a goal of investigating the role played by positive ice albedo feedback in climate dynamics. In this paper we replace the relaxation…

A model system for classical fluids out of equilibrium, referred to as DPD solid (Dissipative Particles Dynamics), is studied by analytical and simulation methods. The time evolution of a DPD particle is described by a fluctuating heat…

The effective action is computed for the \lphi--theory at finite temperature for small perturbations about a constant background field, using a generalized tadpole method. We find the complete effective action, including the real and…

In this paper we consider a model that involves nonlocal diffusion and a classical convective term. Using a scaling argument and a new compactness argument we obtain the first term in the asymptotic behavior of the solutions.

We begin by proving a local existence result for a fractional Caputo nonlocal thermistor problem. Then, additional existence and continuation theorems are obtained, ensuring global existence of solutions.

We provide a simple method for obtaining new Liouville theorems for scaling invariant superlinear parabolic problems with gradient structure. To illustrate the method we prove Liouville theorems (guaranteeing nonexistence of positive…

The asymptotics of a singularly perturbed problem is constructed. describing the transport of a polydisperse impurity in the atmosphere, taking into account the processes of precipitation and wind pick-up, as well as the processes of…

This paper is devoted to reviewing several recent developments concerning certain class of geophysical models, including the primitive equations (PEs) of atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for…

We study the Ericksen-Leslie's parabolic-hyperbolic liquid crystal model in compressible flow. Inspired by our study for incompressible case \cite{Jiang-Luo-arXiv-2017} and some techniques from compressible Navier-Stokes equations, we prove…

In this paper we are concerned with a non-isothermal compressible Navier-Stokes-Fourier model with density dependent viscosity that vanish on the vacuum. We prove the global existence of weak solutions with large data in the…

In this paper we prove the global in time well-posedness of the following non-local diffusion equation with $\alpha \in[0,2/3)$: $$ \partial_t u = {(-\triangle)^{-1}u} \triangle u + \alpha u^2, \quad u(t=0) = u_0. $$ The initial condition…

The Landau--Lifshitz--Baryakhtar (LLBar) equation is a generalisation of the Landau--Lifshitz--Gilbert and the Landau--Lifshitz--Bloch equations which takes into account contributions from nonlocal damping and is valid at moderate…

In this work, we obtain the numerical temperature field to a thermally developing fluid flow inside parallel plates problem with a quantum computing method. The physical problem deals with the heat transfer of a steady state,…