Existence and uniqueness are established for solutions to the viscous conservation law with positive measure initial data when the flux satisfies a p-condition.
Ben-Artzi, Planar Navier-Stokes equations: Vorticity approach , Chapter 5 in ”Handbook of Mathematical Fluid Dynamics, vol
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Viscous Conservation Laws in 1d With Measure Initial Data
Existence and uniqueness are established for solutions to the viscous conservation law with positive measure initial data when the flux satisfies a p-condition.