Consider the equations of Navier-Stokes on ℝn with initial data U0 of the form U0(x) = u0(x) - Mx, where M is an n x n matrix with constant real entries and u0 ∈ L σ p(ℝn). It is shown that under these assumptions the equations of Navier-Stokes admit a unique local solution in Lσ p(ℝn). Moreover, if ∥e tM∥ ≦ 1 for all t ≧ 0, then this mild solution is even analytic in x. This is surprising since the underlying semigroup of Ornstein-Uhlenbeck type is not analytic, in contrast to the Stokes semigroup.
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