Critical Parabolic-Type Problems / / Tomasz W. Dłotko, Yejuan Wang.

• Superior document: Title is part of eBook package: De Gruyter DG Ebook Package English 2020
• VerfasserIn: Dłotko, Tomasz W.,; Wang, Yejuan,
• MitwirkendeR: Dłotko, Tomasz W.,; Wang, Yejuan,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2020]; ©2020
• Year of Publication: 2020
• Language: English
• Series: De Gruyter Series in Nonlinear Analysis and Applications , 34
• Physical Description: 1 online resource (XII, 288 p.)

This self-contained book covers the theory of semilinear equations with sectorial operator going back to the studies of Yosida, Henry, and Pazy, which are deeply extended nowadays. The treatment emphasizes existence-uniqueness theory as a topic of functional analysis and examines abstract evolutionary equations, with applications to the Navier-Stokes system, the quasi-geostrophic equation, and fractional reaction-diffusion equations.

Table of Contents

Frontmatter -- Acknowledgment -- Contents -- 1 Introduction -- 2 Preliminary concepts -- 3 Solvability of the abstract Cauchy problem -- 4 Global in time continuation of solutions -- 5 Definitions, properties, estimates, and inequalities -- 6 Navier–Stokes equation in 2D and 3D -- 7 N-D Navier–Stokes equation, an extended discussion -- 8 Cauchy’s problem for 2-D quasi-geostrophic equation -- 9 Dirichlet’s problem for critical 2D quasi-geostrophic equation -- 10 Dirichlet’s problem for critical Hamilton–Jacobi fractional equation -- 11 Fractional reaction-diffusion equation -- Bibliography -- Index -- Erratum to: Chapter 5 Definitions, properties, estimates, and inequalities -- Erratum to: Chapter 9 Dirichlet’s problem for critical 2D quasi-geostrophic equation -- Erratum to: Chapter 10 Dirichlet’s problem for critical Hamilton-Jacobi fractional equation