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On the uniqueness of bounded weak solutions to the Navier-Stokes Cauchy problem. (English) Zbl 1199.35276

Author’s summary: We give a uniqueness theorem for solutions \((u,\pi)\) to the Navier–Stokes Cauchy problem, assuming that \(u\) belongs to \(L^\infty((0,T)\times \mathbb R^n)\) and \((1+| x| )^{-n-1}\pi\in L^1(0,T;L^1(\mathbb R^n))\), \(n\geq 2\). The interest to our theorem is motivated by the fact that a possible pressure field \(\tilde\pi\) belonging to \(L^1(0,T;\text{BMO})\), satisfies in a suitable sense our assumption on the pressure, and by the fact that the proof is very simple.

MSC:

35Q30 Navier-Stokes equations
35D30 Weak solutions to PDEs
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