A Remark on L ∞ Solutions to the 2-D Navier–Stokes Equations
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A single-exponential growth estimate of the solutions to the 2-dimensional Navier–Stokes equations in the whole space for nondecaying initial velocity is established. The crucial idea is to decompose velocity into high and low frequency parts. Moreover, if the linear term and the vorticity decay exponentially, the velocity is bounded uniformly in time.
Mathematics Subject Classification (2000).35Q30 35Q35
Keywords.2-dimensional Navier–Stokes nondecaying initial velocity vanishing viscosity
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