3 papers
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…
math.AP2025
On well-posedness for non-autonomous parabolic Cauchy problems with rough initial data
Hedong Hou
We establish a complete picture for existence, uniqueness, and representation of weak solutions to non-autonomous parabolic Cauchy problems of divergence type. The coefficients are…
math.AP2024
On regularity of solutions to the Navier--Stokes equation with initial data in
Hedong Hou
We prove that any mild solution in the Koch--Tataru space to the incompressible Navier--Stokes equation with initial data in is weak*-continuous in time, valued…