1. Introduction. Let H be a separable real Hilbert space. We denote the norm on H by |•| and the inner product, by _•,•_. Let C∞(H;0,a) be the set of infinitely smooth H-valued functions on [0,a] (a > 0). We denote the ...

We obtain a criterion of global strong solvability for one class of nonlinear evolution equations in Hilbert space.

We obtain a criterion of global strong solvability for one class of nonlinear evolution equations in Hilbert space.

1. INTRODUCTION Let p ∈ (1, ∞), θ ∈ (−∞, +∞), and a ∈ (0, ∞). Let H be a separable Hilbert space. Denote the norm in H by |•| and the inner product by _•, • _. Let C ∞(H ; 0, a) be the set of H -valued infinitely smooth ...

We study a nonlinear operator differential equation in a Hilbert space. This equation represents an abstract model for the system of Navier–Stokes equations. The main result consists in proving the existence of a strong ...

The system of Navier–Stokes equations can be written in the form of (1), and the well-known problem of the existence of a global strong solution is reduced to a similar problem for abstract equation (1).

Let H be a separable real Hilbert space. The norm in H is denoted by •, and the inner product, by 〈•, •〉. Let C∞(H; 0, a), where a > 0, be the set of infinitely smooth functions on [0, a] with values in H. The completion ...