اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with degenerate heat conductivity
53
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider the one-dimensional compressible Navier-Stokes system with constant viscosity and the nonlinear heat conductivity being proportional to a positive power of the temperature which may be degenerate. This problem is imposed on the stress-free boundary condition, which reveals the motion of a viscous heat-conducting perfect polytropic gas with adiabatic ends putting into a vacuum. We prove that the solution of one dimensional compressible Navier-Stokes system with the stress-free boundary condition shares the same large-time behavior as the case of constant heat conductivity.
قيم البحث
اقرأ أيضاً
We study heat transport in a gas of one-dimensional fermions in the presence of a small temperature gradient. At temperatures well below the Fermi energy there are two types of relaxation processes in this system, with dramatically different relaxati
on rates. As a result, in addition to the usual thermal conductivity, one can introduce the thermal conductivity of the gas of elementary excitations, which quantifies the dissipation in the system in the broad range of frequencies between the two relaxation rates. We develop a microscopic theory of these transport coefficients in the limit of weak interactions between the fermions.
For the free boundary problem of the plasma-vacuum interface to ideal incompressible magnetohydrodynamics (MHD) in two-dimensional space, the a priori estimates of solutions are proved in Sobolev norms by adopting a geometrical point of view. In the
vacuum region, the magnetic field is described by the div-curl system of pre-Maxwell dynamics, while at the interface the total pressure is continuous and the magnetic field is tangent to the boundary. We prove that the $L^2$ norms of any order covariant derivatives of the magnetic field in vacuum and on the boundaries are bounded in terms of initial data and the second fundamental forms of the free interface and the rigid wall.
We study how a system of one-dimensional spin-1/2 fermions at temperatures well below the Fermi energy approaches thermal equilibrium. The interactions between fermions are assumed to be weak and are accounted for within the perturbation theory. In t
he absence of an external magnetic field, spin degeneracy strongly affects relaxation of the Fermi gas. For sufficiently short-range interactions, the rate of relaxation scales linearly with temperature. Focusing on the case of the system near equilibrium, we linearize the collision integral and find exact solution of the resulting relaxation problem. We discuss the application of our results to the evaluation of the transport coefficients of the one-dimensional Fermi gas.
In this article, we study the homogenization limit of a family of solutions to the incompressible 2D Euler equations in the exterior of a family of $n_k$ disjoint disks with centers ${z^k_i}$ and radii $varepsilon_k$. We assume that the initial veloc
ities $u_0^k$ are smooth, divergence-free, tangent to the boundary and that they vanish at infinity. We allow, but we do not require, $n_k to infty$, and we assume $varepsilon_k to 0$ as $kto infty$. Let $gamma^k_i$ be the circulation of $u_0^k$ around the circle ${|x-z^k_i|=varepsilon_k}$. We prove that the homogenization limit retains information on the circulations as a time-independent coefficient. More precisely, we assume that: (1) $omega_0^k = mbox{ curl }u_0^k$ has a uniform compact support and converges weakly in $L^{p_0}$, for some $p_0>2$, to $omega_0 in L^{p_0}_{c}(mathbb{R}^2)$, (2) $sum_{i=1}^{n_k} gamma^k_i delta_{z^k_i} rightharpoonup mu$ weak-$ast$ in $mathcal{BM}(mathbb{R}^2)$ for some bounded Radon measure $mu$, and (3) the radii $varepsilon_k$ are sufficiently small. Then the corresponding solutions $u^k$ converge strongly to a weak solution $u$ of a modified Euler system in the full plane. This modified Euler system is given, in vorticity formulation, by an active scalar transport equation for the quantity $omega=mbox{ curl } u$, with initial data $omega_0$, where the transporting velocity field is generated from $omega$ so that its curl is $omega + mu$. As a byproduct, we obtain a new existence result for this modified Euler system.
For the free boundary problem of the plasma-vacuum interface to three-dimensional ideal incompressible magnetohydrodynamics (MHD), the a priori estimates of smooth solutions are proved in Sobolev norms by adopting a geometrical point of view and some
quantities such as the second fundamental form and the velocity of the free interface are estimated. In the vacuum region, the magnetic fields are described by the div-curl system of pre-Maxwell dynamics, while at the interface the total pressure is continuous and the magnetic fields are tangent to the interface, but we do not need any restrictions on the size of the magnetic fields on the free interface. We introduce the virtual particle endowed with a virtual velocity field in vacuum to reformulate the problem to a fixed boundary problem under the Lagrangian coordinates. The $L^2$-norms of any order covariant derivatives of the magnetic fields both in vacuum and on the boundaries are bounded in terms of initial data and the second fundamental forms of the free interface and the rigid wall. The estimates of the curl of the electric fields in vacuum are also obtained, which are also indispensable in elliptic estimates.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
