Global weak solution of 3D-NSE with exponential damping

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