A new kind of BV entropy solution matching up with the degenerate parabolic equation arising from the two-dimensional Prandtl boundary layer system is introduced. By means of Kruzkov’s bi-variables method, the stability of entropy solutions is proved without any boundary value condition provided that there are some restrictions on the coefficients of the system. For some domains which is regular in a special sense, by the inverse transformation of the Crocco transformation, the two-dimensional Prandtl boundary layer system is well-posedness.
2010 MSC: 35K55; 35R35; 49K40.