H. Pak

activity

20032023

collaborators

5 papers

math.AP2023

Temporal regularity of the solution to the incompressible Euler equations in the end-point critical Triebel-Lizorkin space $F_{1, \infty}^{d + 1} (R^{d})$

Hee Chul Pak

An evidence of temporal dis-continuity of the solution in $F_{1, \infty}^{s} (R^{d})$ is presented, which implies the ill-posedness of the Cauchy problem for the Euler equation…

math.AP2023

Persistence of the solution to the Euler equations in the end-point critical Triebel-Lizorkin space $F_{1, \infty}^{d + 1} (R^{d})$

Hee Chul Pak, Jun Seok Hwang

Local stay of the solutions to the Euler equations for an ideal incompressible fluid in the end-point Triebel-Lizorkin spaces $F_{1, \infty}^{s} (R^{d})$ with $s \geq d + 1$ is…

math.NT2023

Prime numbers as a uniqueness set of the parallelogram equation via the Goldbach's conjecture

Hee Chul Pak, Dongseung Kang

Multiplicative arithmetic functions satisfying the parallelogram functional equation on prime numbers are investigated. It is derived that the unique solution is a quadratic functi…

math.AP2019

Sobolev trace inequality on $W^{s, q} (R^{n})$

Hee Chul Pak

Sobolev trace inequalities on nonhomogeneous fractional Sobolev spaces are established.

math.AP2003

A Compactness Theorem for Homogenization of Parabolic Partial Differential Equations

Hee Chul Pak

In order to have a better description of homogenization for parabolic partial differential equations with periodic coefficients, we define the notion of parametric two-scale conver…

Temporal regularity of the solution to the incompressible Euler equations in the end-point critical Triebel-Lizorkin space F1,∞d+1​(Rd)

Persistence of the solution to the Euler equations in the end-point critical Triebel-Lizorkin space F1,∞d+1​(Rd)

Prime numbers as a uniqueness set of the parallelogram equation via the Goldbach's conjecture

Sobolev trace inequality on Ws,q(Rn)

A Compactness Theorem for Homogenization of Parabolic Partial Differential Equations

Temporal regularity of the solution to the incompressible Euler equations in the end-point critical Triebel-Lizorkin space $F_{1, \infty}^{d + 1} (R^{d})$

Persistence of the solution to the Euler equations in the end-point critical Triebel-Lizorkin space $F_{1, \infty}^{d + 1} (R^{d})$

Sobolev trace inequality on $W^{s, q} (R^{n})$