Existence of global entropy solutions to general system of Keyfitz–Kranzer type

Abstract

In this paper, we apply the div–curl lemma in the compensated compactness theory (Tartar, 1979 [38], Murat, 1978 [34]) to the special pair of functions (c,wiε(x,t)) to obtain a very short proof of the existence of global entropy solutions for quite general system (1.1) of Keyfitz–Kranzer type (Keyfitz and Kranzer, 1980 [24]), where c is a constant and wiε(x,t) are variants in (1.1). This work extends in some sense the previous work by the author (Lu, 2011 [32]) for a special system of Keyfitz–Kranzer or Aw–Rascle type. As a by-product, a simple proof of the existence and stability of entropy solutions is also obtained for the hyperbolic system of isentropic gas dynamics in Eulerian coordinates under the compactness assumption of uxε(x,t) or ρxε(x,t) in Wloc−1,α(R×R+), α∈(1,2), where uε(x,t), ρε(x,t) are viscosity velocity and density.