TY - JOUR
T1 - The global existence and large time behavior of smooth compressible fluid in an infinitely expanding ball, III
T2 - The 3-D Boltzmann equation
AU - Yin, Huicheng
AU - Zhao, Wenbin
PY - 2018/1/5
Y1 - 2018/1/5
N2 - This paper is a continuation of the works in [35] and [37], where the authors have established the global existence of smooth compressible flows in infinitely expanding balls for inviscid gases and viscid gases, respectively. In this paper, we are concerned with the global existence and large time behavior of compressible Boltzmann gases in an infinitely expanding ball. Such a problem is one of the interesting models in studying the theory of global smooth solutions to multidimensional compressible gases with time dependent boundaries and vacuum states at infinite time. Due to the conservation of mass, the fluid in the expanding ball becomes rarefied and eventually tends to a vacuum state meanwhile there are no appearances of vacuum domains in any part of the expansive ball, which is easily observed in finite time. In the present paper, we will confirm this physical phenomenon for the Boltzmann equation by obtaining the exact lower and upper bound on the macroscopic density function.
AB - This paper is a continuation of the works in [35] and [37], where the authors have established the global existence of smooth compressible flows in infinitely expanding balls for inviscid gases and viscid gases, respectively. In this paper, we are concerned with the global existence and large time behavior of compressible Boltzmann gases in an infinitely expanding ball. Such a problem is one of the interesting models in studying the theory of global smooth solutions to multidimensional compressible gases with time dependent boundaries and vacuum states at infinite time. Due to the conservation of mass, the fluid in the expanding ball becomes rarefied and eventually tends to a vacuum state meanwhile there are no appearances of vacuum domains in any part of the expansive ball, which is easily observed in finite time. In the present paper, we will confirm this physical phenomenon for the Boltzmann equation by obtaining the exact lower and upper bound on the macroscopic density function.
KW - Boltzmann equation
KW - Expanding ball
KW - Global existence
KW - Vacuum state
KW - Weighted energy estimate
UR - http://www.scopus.com/inward/record.url?scp=85028993686&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85028993686&origin=recordpage
U2 - 10.1016/j.jde.2017.08.064
DO - 10.1016/j.jde.2017.08.064
M3 - 21_Publication in refereed journal
AN - SCOPUS:85028993686
VL - 264
SP - 30
EP - 81
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 1
ER -