ABSTRACT
As was mentioned in Introduction, after the publication of results by S.L.Sobolev, I.G.Petrovsky emphasized the importance of the study of general differential equations and systems not solved relative to the higherorder time-derivative. The first deep investigation in this direction was due to S.A.Galpern [1-3] who constructed the L2theory for the Cauchy problem for systems of the form
Later, K.K.Golovkin [1, 2], O.A.Ladyzhenskaya [1, 2], V.N.Maslennikova [1, 2], V.A.Solonnikov [1, 3], and others established the Lp-estimates and estimates in the Hölder norms for solutions to the Cauchy problem for some systems in hydrodynamics of the form (0.1).
