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Books for the Course

This book [1] is for ordinary differential equation. There should also exist an En- glish version in the net. For semigroup theory I recommend [4], [3], [2]. Similar this bookhttps://www.emis.de/monographs/Chueshov/book.pdfThis book [6] deals with the Navier Stokes equations. It gives a good introduction for function spaces and weak derivatives. Many examples for linear and nonlinear partial differential equations one can find in [5].

References

[1] Herbert Amann.Gew¨ohnliche Differentialgleichungen. de Gruyter Lehrbuch.

[de Gruyter Textbook]. Walter de Gruyter & Co., Berlin, 1983.

[2] Klaus-Jochen Engel and Rainer Nagel. A short course on operator semi- groups. Universitext. Springer, New York, 2006.

[3] Alessandra Lunardi.Analytic semigroups and optimal regularity in parabolic problems, volume 16 of Progress in Nonlinear Differential Equations and their Applications. Birkh¨auser Verlag, Basel, 1995.

[4] A. Pazy.Semigroups of linear operators and applications to partial differen- tial equations, volume 44 ofApplied Mathematical Sciences. Springer-Verlag, New York, 1983.

[5] George R. Sell and Yuncheng You. Dynamics of evolutionary equations, volume 143 ofApplied Mathematical Sciences. Springer-Verlag, New York, 2002.

[6] Hermann Sohr. The Navier-Stokes equations. Birkh¨auser Advanced Texts: Basler Lehrb¨ucher. [Birkh¨auser Advanced Texts: Basel Textbooks].

Birkh¨auser Verlag, Basel, 2001. An elementary functional analytic approach.

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