Global weak solution of 3D-NSE with exponential damping

In this paper, we prove the global existence of incompressible Navier-Stokes equations with damping α ( e β ∣ u ∣ 2 − 1 ) u α ({e}^{β | u{| }²}-1)u , where we use the Friedrich method and some new tools. The delicate problem in the construction of a global solution is the passage to the limit in exponential nonlinear term. To solve this problem, we use a polynomial approximation of the damping part and a new type of interpolation between L ∞ ( R + , L 2 ( R 3 ) ) {L}∞({{R}}⁺,{L}²({{R}}³)) and the space of functions f f such that ( e β ∣ f ∣ 2 − 1 ) ∣ f ∣ 2 ∈ L 1 ( R + × R 3 ) ({e}^{β | f{| }²}-1)| f{| }²∈ {L}¹({{R}}⁺× {{R}}³) . Fourier analysis and standard techniques are used.