ИСТИНА

The talk will be devoted to the normal parabolic equation (NPE) connected with 3D Helmholtz system whose nonlinear term B(v) is orthogonal projection of nonlinear term for Helmholtz system on the ray generated by vector v. To study NPE of such kind is interesting by the following reasons: 1) Its study open the way to construct the method of nonlocal stabilization by feedback control for 3D Helmholtz as well as for 3D Navier-Stokes equations. 2) Its study can help to understand better difficulties that one should overcome to solve Millenium problem on non local existence of smooth solution for 3D Navier-Stokes equations. The structure of dynamical flow corresponding to this NPE will be described. Besides, the non local stabilization problem for NPE by starting control supported on arbitrary fixed subdomain will be formulated. The main steps of solution to this problem will be discussed. At last how to apply this result for solution of nonlocal stabilization problem with impulse control for 3D Helmholtz system will be explained.