LANL e-print math.AP/0203230

the finite momentum of inertia). As well known, the solution to the Cauchy problem for system (1-3) may lose the initial smoothness in a finite time, sometimes there is a possibility to estimate the time of singularity formation from above (see, f.e., [1] and references therein). Moreover, in the case more frequently investigated f = 0 the compactly supported initial data are sufficient for the further singularity formation. (f.e., [2]). At the same time it is interesting that there are some nontrivial classes of globally smooth solutions. Note that if f = 0, the components of such solutions do not belong to the Sobolev class. The paper is organized as follows. Firstly supposing the existence of globally in time smooth solution having concrete properties (denote it U0), we show that if we choose some initial data (CD1) close in the Sobolev norm to initial data of such solution (CD0), then the corresponding solution to the Cauchy problem (U1) occurs globally smooth as well. Then we show that the solutions U0 with such kind of properties exists, moreover, at n = 2 we construct some of them. The present work may be considered as a continuation of papers [3], [4], and their generalization in some sense.