论文标题
散热器的全局耗散解决方案，从
Global dissipative solutions of the defocusing isothermal Euler-Langevin-Korteweg equation
论文作者
论文摘要
我们在defocersion的三个散热器上构建了全局耗散溶液在尺寸的圆环上，从而将等温欧拉 - 洛格温vin-korteweg系统构造，该系统对应于具有等温压力定律的Euler-korteweg系统，可压缩量子流体的Euler-korteweg系统，与速度相对于线性拖动项。特别是，等温特征可防止能量和BD渗透率为阳性。调整标准近似参数，我们首先显示了使用等温线navier-stokes-langevin-korteweg系统的全局弱解决方案。然后引入满足Gronwall型不平等的相对熵函数，然后执行Inviscid限制，以获得Euler-Langevin-Korteweg系统的耗散溶液的存在。
We construct global dissipative solutions on the torus of dimension at most three of the defocusing isothermal Euler-Langevin-Korteweg system, which corresponds to the Euler-Korteweg system of compressible quantum fluids with an isothermal pressure law and a linear drag term with respect to the velocity. In particular, the isothermal feature prevents the energy and the BD-entropy from being positive. Adapting standard approximation arguments we first show the existence of global weak solutions to the defocusing isothermal Navier-Stokes-Langevin-Korteweg system. Introducing a relative entropy function satisfying a Gronwall-type inequality we then perform the inviscid limit to obtain the existence of dissipative solutions of the Euler-Langevin-Korteweg system.
