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2014 Reprint of 1963 version. complete facsimile of the unique variation, now not reproduced with Optical acceptance software program. Olga Aleksandrovna Ladyzhenskaya used to be a Soviet and Russian mathematician. She was once identified for her paintings on partial differential equations (especially Hilbert's nineteenth challenge) and fluid dynamics. She supplied the 1st rigorous proofs of the convergence of a finite distinction procedure for the Navier-Stokes equations. this can be a revised and up to date version of a e-book of primary significance within the rigorous conception of options of the Navier-Stokes equations. the writer considers the questions in their lifestyles and forte while fulfilling acceptable boundary stipulations. For this function she extends the category of permissible services from the infinitely differentiable classification (classical strategies) to a category of generalized services outlined within the distributional experience. hence life of answer within the new type is an important yet now not enough for lifestyles within the classical feel. Linear and non-linear, regular and unsteady varieties of the equations and either finite and limitless domain names are all thought of: in every one form of challenge very important theorems are tested during which many new rules and strategies are constructed. The booklet is strongly advised to mathematicians drawn to smooth research and the rigorous idea of fluid mechanics.

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