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Using effective field theory methods, we calculate the low-temperature phonon thermal partition function for a generic superfluid, thus providing the leading thermal corrections to a superfluid's equation of state, thermodynamic quantities,…
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…
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…
We derive two different generalized heat-transport equations: The most general one, of the first order in time and second order in space, encompasses some well known heat equations and describes the hyperbolic regime in the absence of…
A quantum thermodynamic system can conserve non-commuting observables, but the consequences of this phenomenon on relaxation are still not fully understood. We investigate this problem by leveraging an observable-dependent approach to…
In this paper, we study the Cauchy problem for a nonlinear wave equation with frictional and viscoelastic damping terms. As is pointed out by [8], in this combination, the frictional damping term is dominant for the viscoelastic one for the…
The full compressible magnetohydrodynamic system in three-dimensional exterior domains is investigated. For the initial-boundary-value problem of this system with slip boundary condition for the velocity, adiabatic one for the temperature,…
We prove approach to thermal equilibrium for the fully Hamiltonian dynamics of a dynamical Lorentz gas, by which we mean an ensemble of particles moving through a $d$-dimensional array of fixed soft scatterers that each possess an internal…
The second law of thermodynamics is a useful and universal tool to derive the generalizations of the Fourier's law. In many cases, only linear relations are considered between the thermodynamic fluxes and forces, i.e., the conduction…
In the present paper we consider a porous thermoelastic system with only one dissipative mechanism generated by the heat conductivity modelled by the Gurtin-Pipkin thermal law. By the use of a semigroup approach and the Lumer-Phillips…
In this paper we address the temperature patch problem of the 2D viscous Boussinesq system without heat diffusion term. The temperature satisfies the transport equation and the initial data of temperature is given in the form of…
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We consider a class of $L^1$ critical nonlocal aggregation equations with linear or nonlinear porous media-type diffusion which are characterized by a long-range interaction potential that decays faster than the Newtonian potential at…
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A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of the distribution function. Assuming enough initial moments…
The quantum dynamics away from equilibrium is of fundamental interest for interacting many-body systems. In this letter, we study tilted many-body systems using the effective Hamiltonian derived from the microscopic description. We first…
We generalize thermal WIMP (Weakly Interacting Massive Particle) freeze-out within Tsallis nonextensive statistics. Using Curado-Tsallis $q$-distributions $f_q(E;\mu,T)$ we compute $q$-deformed number and energy densities, pressure, entropy…
The system of compressible adiabatic flow through porous media is considered in $\mathbb{R}^{3}$ in the present paper. The global existence and uniqueness of classical solutions are obtained when the initial data is near its equilibrium. We…