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Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity

Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第10期8卷 1681-1690页

作者： ZHANG Ting FANG Dao-yuan Department of Mathematics Zhejiang University Hangzhou 310027 China

We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove that the weak solutions to these systems do not exhibit vacuum states, provided that no vacuum states are present initially. The essential re- quirements on the solutions are that the mass and energy of the fluid are locally integrable at each time, and the Lloc1-norm of the velocity gradient is locally integrable in time.

关键词： Compressible Navier-Stokes equations vacuum states Density-dependent viscosity

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Relic Entropy Growth and Initial Big Bang Conditions, as a Subset of Quantum Information

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Journal of High Energy Physics, Gravitation and Cosmology 2016年第3期2卷 392-411页

作者： Andrew W. Beckwith Department of Physics Chongqing University Chongqing China

This paper shows how increased entropy values from an initially low big bang level can be measured experimentally by counting relic gravitons. Furthermore the physical mechanism of this entropy increase is explained via analogies with early-universe phase transitions. The role of Ng’s revised infinite quantum statistics in the physics of gravitational wave detection is acknowledged. Ng’s infinite quantum statistics can be used to show that is a starting point to the increasing net universe cosmological entropy. Finally, in a nod to similarities with zero point energy (ZPE) analysis, it is important to note that the resulting in fact is much lower, allowing for evaluating initial graviton production as an emergent field phenomena, which may be similar to how ZPE states can be used to extract energy from a vacuum if entropy is not maximized. The rapid increase in entropy so alluded to without near sudden increases to 1088 may be enough to allow successful modeling of relic graviton production for entropy in a manner similar to zero point energy (ZPE) energy extraction from a vacuum state. This entropy count is akin to quantum information models used to tell how much “information” may be stored in initial conditions, and transferred from a prior to the present

关键词： Entropy Cosmic Singularity Zero Point Energy (ZPE) Emergent Fields Gravitons vacuum states Quantum Information states Anti de Sitter Correspondence with Conformal Field Theory (Ads/CFT)

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THE VANISHING PRESSURE LIMIT OF SOLUTIONS TO THE SIMPLIFIED EULER EQUATIONS FOR ISENTROPIC FLUIDS

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Annals of Differential Equations 2012年第1期28卷 115-126页

作者： Qingling Zhang (School of Math.and Computer Sciences,Jianghan University,Wuhan 430056)

In this paper,the Riemann problem of the 1-D reduced model for the 2-D Euler equations is considered and the Riemann solutions are *** is proved that,as the pressure vanishes,they converge to two kinds of Riemann solu... 详细信息

关键词： Euler equations transport equations measure solutions δ-shocks vacuum states

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