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A remark on the Stokes problem in Lorentz spaces

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  • We study the Stokes initial boundary value problem with an initial data in a Lorentz space. We develop a suitable technique able to solve the problem and to prove the semigroup properties of the resolving operator in the case of the ''limit exponents''. The results are a completion of the ones related to the usual $L^p$-theory, of the ones already known and they are also useful tool to study some questions related to the Navier-Stokes equations.
    Mathematics Subject Classification: 35Q30, 76D05, 76D03.


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