相关论文: Power concavity and Dirichlet heat flow
Thermal conduction has been suggested as a possible mechanism by which sufficient extra heating is provided in radiation-dominated accretion flows. We consider the extreme case in which the generated energy due to the viscosity and the…
The fundamental gap of a domain is the difference between the first two eigenvalues of the Laplace operator. In a series of recent and celebrated works, it was shown that for convex domains in $\mathbb R^n$ and $\mathbb S^n$ with Dirichlet…
In this short note, we prove that $\alpha$-concavity of the pressure is not preserved for the porous medium equation in dimensions $n=3$ and higher for any $\alpha\in [0,1]\backslash \{\frac{1}{2}\}$. Together with the result of…
We consider the Dirichlet problem for a compressible two-fluid model in three dimensions, and obtain the global existence of weak solution with large initial data and independent adiabatic constants \Gamma,\gamma>=9/5. The pressure…
We show that for any $\al<\frac 17$ there exist $\al$-H\"older continuous weak solutions of the three-dimensional incompressible Euler equation, which satisfy the local energy inequality and strictly dissipate the total kinetic energy. The…
We introduce the transportation-annihilation distance $W_p^\sharp$ between subprobabilities and derive contraction estimates with respect to this distance for the heat flow with homogeneous Dirichlet boundary conditions on an open set in a…
In an attempt to understand the properties of convective energy transport in the solar convection zone, a numerical model has been constructed for turbulent flows in a compressible, radiation-coupled, non-magnetic, gravitationally…
In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcy's law. We show formation of singularities with infinite energy and for finite energy we obtain…
The non-equilibrium thermodynamics of relativistic systems have a rich phenomenology. The simplest phenomenon in the class of dissipative processes is that of heat. This letter presents a brief summary of the efforts made to tackle the…
It is a basic property of the entropy in statistical physics that is concave as a function of energy. The analog of this in representation theory would be the concavity of the logarithm of the multiplicity of an irreducible representation…
We consider two non-interacting systems embedded in a heat bath. If they remain dynamically independent, physical inconsistencies are avoided only if the single-system reduced dynamics is completely positive also beyond the weak-coupling…
In this paper, we establish the existence of strong solutions to the steady non-isentropic compressible Navier-Stokes system with Dirichlet boundary conditions in bounded domains where the fluid is driven by the wall temperature, and…
The downward flow in a vertical duct with one heated and three thermally insulated walls is analyzed numerically using the two-dimensional approximation valid in the asymptotic limit of an imposed strong transverse magnetic field. The work…
We study turbulent natural convection in enclosures with conjugate heat transfer. The simplest way to increase the heat transfer in this flow is through rough surfaces. In numerical simulations often the constant temperature is assigned at…
We investigate the two-dimensional transport of heat through viscous flow between two parallel rough interfaces with a given fractal geometry. The flow and heat transport equations are solved through direct numerical simulations, and for…
Viscous dissipation causes significant energy losses in fluid flows; in ducts, laminar flows provide the minimum resistance to the motion, whereas turbulent currents substantially increase the friction at the wall and the energy requirement…
For the discretization of the convective term in the Navier-Stokes equations (NSEs), the commonly used convective formulation (CONV) does not preserve the energy if the divergence constraint is only weakly enforced. In this paper, we apply…
Non-radiating, advection-dominated, accretion flows are convectively unstable. We calculate the two-dimensional (r-theta) structure of such flows assuming that (1) convection transports angular momentum inwards, opposite to normal viscosity…
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.…
Onsager conjectured that weak solutions of the Euler equations for incompressible fluids in 3D conserve energy only if they have a certain minimal smoothness, (of order of 1/3 fractional derivatives) and that they dissipate energy if they…