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We establish the local-in-time well-posedness of classical solutions to thevacuum free boundary problem of the viscous Saint-Venant system for shallowwaters derived rigorously from incompressible Navier-Stokes system with amoving free surface by Gerbeau-Perthame. Our solutions (the height andvelocity) are smooth (the solutions satisfy the equations point-wisely) all theway to the moving boundary, although the height degenerates as a singularity ofthe distance to the vacuum boundary. The proof is built on some newhigher-order weighted energy functional and weighted estimates associated tothe degeneracy near the moving vacuum boundary.

Well-posedness of classical solutions to the vacuum free boundary problem of the viscous Saint-Venant system for shallow waters