(Ebook) Analysis of the Navier-Stokes Problem: Solution of a Millennium Problem, 2nd Edition by Alexander G. Ramm ISBN 9783031307225, 3031307224

(Ebook) Analysis of the Navier-Stokes Problem: Solution of a Millennium Problem, 2nd Edition by Alexander G. Ramm ISBN 9783031307225, 3031307224

This book explains the history of the Navier-Stokes Problem (NSP). This new edition includes the author's theory for solving integral equations with hyper-singular kernels and new results on the Laplace transform. An a priori estimate of the solution to the NSP is derived. The author then proves the NSP paradox: if a solution of the NSP exists and its initial data are smooth, rapidly decaying, and not equal to zero identically, then the author proves that the initial data are equal to zero identically. This result yields a solution of the millennium problem concerning the Navier-Stokes equations: the NSP in the three-dimensional space without boundaries does not have a solution defined for all time unless the initial data are equal to zero identically. Therefore, the NSP is physically and mathematically contradictive. This calls for a new theory of the viscous incompressible fluid motion that is free from contradictions.