Abstract: We shall compare the solution of the Caucky problem
u_t+(v^-1)_x=0 v_t-u_x=0 (1.1)
(u,v)(0,x)=(u₀(x),v₀(x)) (1.2) with the solution of the corresponding Riemann problem (1.1) with the initial data
(u,v)(0,x)=(u_-,v_-) for x<0 (u₊,v₊) for x>0 (1.2)' in the whole t>0 half plane.The system of equations (1.1) is the mathematical modol for isentropic gas dynamics with adiabatic exponent x=1 Here v is tlie specific volume v=(1)/ρ,ρ is the density and u is the speed of the gas (u_∓,v_∓)=lim_x→∓∞(u₀(x),v₀(x)).