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   Kedlaya, Kiran S (June 2022, Cambridge University Press)

   Now in its second edition, this volume provides a uniquely detailed study of $$P$$-adic differential equations. Assuming only a graduate-level background in number theory, the text builds the theory from first principles all the way to the frontiers of current research, highlighting analogies and links with the classical theory of ordinary differential equations. The author includes many original results which play a key role in the study of $$P$$-adic geometry, crystalline cohomology, $$P$$-adic Hodge theory, perfectoid spaces, and algorithms for L-functions of arithmetic varieties. This updated edition contains five new chapters, which revisit the theory of convergence of solutions of $$P$$-adic differential equations from a more global viewpoint, introducing the Berkovich analytification of the projective line, defining convergence polygons as functions on the projective line, and deriving a global index theorem in terms of the Laplacian of the convergence polygon. 

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2. Solutions of KZ differential equations modulo p

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   We construct polynomial solutions of the KZ differential equations over a finite field F_p as analogs of hypergeometric solutions. 

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3. Existence of weak solutions to $ p $-Navier-Stokes equations

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   Feng, Yuanyuan; Li, Lei; Liu, Jian-Guo; Xu, Xiaoqian (January 2024, Discrete and Continuous Dynamical Systems - B)
4. Thouless–Anderson–Palmer equations for generic $$p$$-spin glasses

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   Auffinger, Antonio; Jagannath, Aukosh (July 2019, The Annals of Probability)
5. Existence of global weak solutions of $ p $-Navier-Stokes equations

   https://doi.org/10.3934/dcdsb.2021051  

   Liu, Jian-Guo; Zhang, Zhaoyun (January 2022, Discrete & Continuous Dynamical Systems - B)

   This paper investigates the global existence of weak solutions for the incompressible \begin{document}$ p $$\end{document}-Navier-Stokes equations in \begin{document}$$ \mathbb{R}^d $$\end{document} \begin{document}$$ (2\leq d\leq p) $$\end{document}. The \begin{document}$$ p $$\end{document}-Navier-Stokes equations are obtained by adding viscosity term to the \begin{document}$$ p $$\end{document}-Euler equations. The diffusion added is represented by the \begin{document}$$ p $$\end{document}-Laplacian of velocity and the \begin{document}$$ p $$\end{document}-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-\begin{document}$$ p $$\end{document}$ distances with constraint density to be characteristic functions. 

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