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This book is concerned with the 3D Navier-Stokes equations with damping(DNS). We've obtained some important results such as the uniqueness of the weak solutions and the existence of the strong solutions while studying DNS for several years.In the current edition, we synthesis and analysis these results as well as make our effort to give the proofs of them in detail and perfectly. However, in this process, we have benefited enormously.In conclusion, I hope that the interested scientist will enjoy this book and derive great benefit from reading it just as I did while writing it.