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(eβ∣u∣2−1)u\alpha \left({e}^{\beta | 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+,L2(R3)){L}^{\infty }\left({{\mathbb{R}}}^{+},{L}^{2}\left({{\mathbb{R}}}^{3})) and the space of functions ff such that (eβ∣f∣2−1)∣f∣2∈L1(R+×R3)\left({e}^{\beta | f{| }^{2}}-1)| f{| }^{2}\in {L}^{1}\left({{\mathbb{R}}}^{+}\times {{\mathbb{R}}}^{3}). Fourier analysis and standard techniques are used.

Keywords

• navier-stokes equations
• friedrich method
• weak solution
• 35-xx
• 35q30
• 76d05
• 76n10