Geodesic
Smoothness in the viscosity of solutions of nonlinear differential equations in a Banach space
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 99-103.

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The analytical properties of solutions of differential equations with a small parameter form the basis of analytical perturbation theory. In the case of a regular theory, Poincaré's decomposition theorems or statements that follow from the concept of an analytic family in the sense of Kato hold. For singularly perturbed problems, the approach based on S. A. Lomov's regularization method is useful; the central concept of this method is the concept of a pseudoanalytic (pseudoholomorphic) solution, i.e., a solution, which can be represented in the form of a series converging in the usual sense in powers of a small parameter.
Keywords: Navier–Stokes-type equation, pseudoholomorphic solution, monotone system of norms. 
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V. I. Kachalov. Smoothness in the viscosity of solutions of nonlinear differential equations in a Banach space. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 99-103. http://geodesic.mathdoc.fr/item/INTO_2021_193_a9/

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