6 papers · 1 filter
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…
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…
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…
On well-posedness for parabolic Cauchy problems of Lions type with rough initial data
Pascal Auscher, Hedong Hou
We establish a complete picture for well-posedness of parabolic Cauchy problems with time-independent, uniformly elliptic, bounded measurable complex coefficients. We exhibit a ran…
On well-posedness and maximal regularity for parabolic Cauchy problems on weighted tent spaces
Pascal Auscher, Hedong Hou
We prove well-posedness in weighted tent spaces of weak solutions to the Cauchy problem , where the source also lies in (dif…
On representation of solutions to the heat equation
Pascal Auscher, Hedong Hou
We propose a simple method to obtain semigroup representation of solutions to the heat equation using a local condition with prescribed growth and a boundedness condition wit…