2 x 2 hyperbolic systems of conservation laws in classes of functions of bounded p-variation

In this paper, we consider 2 × 2 hyperbolic systems of conservation laws in one space dimension with characteristic fields satisfying a condition that encompasses genuine nonlinearity and linear degeneracy as well as intermediate cases, namely, with standard notations, rᵢ· ∇ λᵢ ≥ 0. We prove the existence of entropy solutions in the fractional $BV$ spaces Wₚ(R) of functions of bounded p-variation, p ∈ [1,3/2], for small initial data.