Existence of global solutions for isentropic gas flow with friction. (5th June 2020)

• Record Type: Journal Article
• Authors: Lu, Yun-guang
• Is Part Of: Nonlinearity. Volume 33:Number 8(2020)
• Page Start: 3940
• Page End: 3969
• Publication Date: 2020-06-05
• Subjects: global weak solution -- isentropic gas dynamics -- friction -- flux approximation -- compensated compactness -- Laval nozzle; 35L45, 35L60, 46T99; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ab7d20
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper, we study the existence of global entropy solutions for the Cauchy problem of the extended river flow system with a friction α ( x ) depending on the space variable x . First, under the boundedness of | α ( x ) | L 1 ( R ), we apply the viscosity-flux approximation method coupled with the maximum principle to obtain the a priori L ∞ estimates for the approximation solutions. Second, we prove the pointwise convergence of the approximation solutions by using the compactness framework from the compensated compactness theory. Finally, as a by-product, we obtain the existence of global solutions for isentropic gas flow in the Laval nozzle with friction.