5 papers · 1 filter
Maximal regularity and caloric trace estimates in mixed Lebesgue norms for the heat equation
Hui Chen, Su Liang, Tai-Peng Tsai
We study the heat equation in the half-space with nonhomogeneous Dirichlet boundary data. For the caloric extension of the boundary data , we prove maximal regularity estima…
Remarks on the maximal regularity for parabolic boundary value problems with inhomogeneous data
Hui Chen, Su Liang, Tai-Peng Tsai
Inspired by Ogawa-Shimizu [JEE 2022] and Chen-Liang-Tsai [IMRN 2025] on the second and first order derivative estimates of solution of heat equation in the upper half space with bo…
The local regularity theory for the Stokes and Navier--Stokes equations near the curved boundary
Hui Chen, Su Liang, Tai-Peng Tsai
In this paper, we study local regularity of the solutions to the Stokes equations near a curved boundary under no-slip or Navier boundary conditions. We extend previous boundary es…
Poisson kernel and blow-up of the second derivatives near the boundary for Stokes equations with Navier boundary condition
Hui Chen, Su Liang, Tai-Peng Tsai
We derive the explicit Poisson kernel of Stokes equations in the half space with nonhomogeneous Navier boundary condition (BC) for both infinite and finite slip length. By using th…
Gradient estimates for the non-stationary Stokes system with the Navier boundary condition
Hui Chen, Su Liang, Tai-Peng Tsai
For the non-stationary Stokes system, it is well-known that one can improve spatial regularity in the interior, but not near the boundary if it is coupled with the no-slip boundary…