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math.AP2026
Global existence of smooth solutions to the Navier-Stokes equations for initial data with infinite energy
Alexey Cheskidov, Hedong Hou
We prove the global existence of solutions to the Navier-Stokes equations for any divergence-free distributional initial data. The solutions are smooth in both time and space at po…
math.CA2026
Form domination and tent space estimates for operators on the half-space
Pascal Auscher, Hedong Hou, Emiel Lorist +1
We study operators acting on functions defined on the half-space, with methods inspired by sparse domination. Using the specific link between dyadic grids on the boundary and Whitn…
math.AP2026
On non-uniqueness of mild solutions and stationary singular solutions to the Navier-Stokes equations
Alexey Cheskidov, Hedong Hou
We prove that the unconditional uniqueness of mild solutions to the Navier-Stokes equations fails in all the Besov spaces with negative regularity index, by constructing non-trivia…