During the three days of November 21-23, 2018, the Winter School on Evolution Equations and Application has taken place, in which the advanced students listened to three lecture series taught by three lecturers from universities in Vietnam and Germany. Concretely:

- Prof. Matthias Hieber (Technical University of Darmstadt and Vice Director of the Mathematical Research Institute of Oberwolfach, Germany) lectured on the strong periodic solutions of linear, semi-linear, and quasi-linear equations. The maximum periodic regularity theorems for general evolution equations are covered in detail. Concrete applications to the Keller-Segel model of chemotaxis and the bi-domain problem of electro-physiology and related models are presented explicitly.

- Dr. Pham Trieu Duong (Hanoi National University of Education) introduced some fundamental approaches related to Fourier transforms and pseudo-differential operators to study the existence and uniqueness of solutions of structural-damped wave equations containing the fractional Laplace operator, Fujita-type critical exponents, and problems associated to Strauss conjecture. These are important issues that have been concerned and developed strongly by the hyperbolic equation community in recent years.

- Assoc. Prof. Nguyen Thieu Huy (Hanoi University of Science and Technology) presented a modeling that leads to the Navier-Stokes equations for fluid dynamics, Kato iteration methods to prove the existence and uniqueness of a mild solutions in the whole space. Furthermore, theorems on stability and periodicity of solutions based on Massera’s and Serrin’s principle have also been introduced in detail. Recent results on the stability and periodicity of solutions to Navier-Stokes equations on non-compact Einstein manifolds with negative Ricci curvature are also presented explicitly.