Research Interests : Machine learning, Partial differential equation

• • Deep learning for inverse problem

  • Nonlinear dispersive equation

    • Fractional Schrödinger equation

    • Probabilistic well-posedness on $\mathbb{R}^d$

  • Nonlinear elliptic equation

    • Cafarelli-Kohn-Nirenberg Inequality

Submitted for Publications

• 1. M Haltmeier, G Hwang, "ECALL: Expectation-calibrated learning for unsupervised blind deconvolution"

Refereed Journal Publications

• 1. G Hwang, M Kar, "Reconstructing unknown inclusions for the biharmonic equation",  Journal of Mathematical Analysis and Applications 530 (2), 127745

  2. G Hwang, H Yoon, "Probabilistic local wellposedness of 1D quintic NLS below L2 (R)", Journal of Mathematical Analysis and Applications 527 (1), 127195

  3. JL Chern, M Hashizume, G Hwang,  "Existence and non-existence of minimizers for Hardy-Sobolev type inequality with Hardy potentials",  Applicable Analysis, 1-15

  4. Y Jung, H Kim, G Hwang, SH Baek, S Lee, "Mesh density adaptation for template-based shape reconstruction", ACM SIGGRAPH 2023 Conference Proceedings, 1-10

  5. G Ju, Y Choi, D Lee, JH Paik, G Hwang, S Lee, "Self-Supervised Dehazing Network Using Physical Priors", Asian Conference on Computer Vision, 290-305

  6. JL Chern, G Hwang, J Takahashi and E Yanagida, "On the evolution equation with a dynamic Hardy-type potential", Journal of Evolution Equations 21 (2), 2141-2165

  7. JL Chern, CH Chen and G Hwang, "Structure of minimizers of cafarelli-kohn-nirenberg inequality", Tohoku Mathematical Journal 72 (4), 551-567

  8. JL Chern, M Hashizume and G Hwang, "Properties of solutions to semilinear elliptic problem with Hardy potential", Journal of Differential Equations 269 (2), 1432-1464

  9. G Hwang, "Well-posedness and Scattering for the Critical Fractional Schrödinger Equations", Funkcialaj Ekvacioj 63 (2), 231-245

  10. G Hwang, "Probabilistic well-posedness of the mass-critical NLS with radial data below L2 (Rd)", Journal of Mathematical Analysis and Applications 475 (2), 1842-1854

  11. M Hashizume, CH Hsia and G Hwang, "On the Neumann Problem of Hardy-Sobolev critical equations with the multiple singularities", Communications on Pure and Applied Analysis 18 (1), 301–322

  12. G Hwang, "Almost Sure Well-Posedness of Fractional Schrödinger Equations with Hartree Nonlinearity", Publications of the Research Institute for Mathematical Sciences 54 (1), 1-45

  13. G Hwang and C Kwak, "Probabilistic well-posedness of generalized KdV", Proceedings of the American Mathematical Society 146 (1), 267-280

  14. Y Cho, G Hwang and C Yang, "On the modified scattering of 3-D Hartree type fractional Schrödinger equations with Coulomb potential", Adv. Differential Equations. 23 (2018), no. 9-10, 649-692

  15. Y Cho, G Hwang and T Ozawa, "On the focusing energy-critical fractional nonlinear Schrödinger eqautions", Adv. Differential Equations 23 (2018), no. 3-4, 161–192

  16. G Hwang, "Almost sure wellposedness of fractional Schrödinger equations with Hartree nonlinearity", Publ. Res. Inst. Math. Sci. 54 (2018), no. 1, 1–44

  17. G Hwang and C Kwak, "Probabilistic well-posedness of generalized KdV", Proc. Amer. Math. Soc. 146 (2018), no. 1, 267-280

  18. Y Cho, G Hwang and T Ozawa, "Corrigendum to "On small data scattering of Hartree equations with short-range interaction" [Comm. Pure. Appl. Anal., 15 (2016), 1809--1823]", Commun. Pure. Appl. Anal Vol.16, Issue 5, 2017, 1939-1940

  19. Y Cho, G Hwang and T Ozawa, "On small data scattering of Hartree equations with short-range interaction", Commun. Pure. Appl. Anal Vol.15, Issue 5, 2016, 1809-1823

  20. Y Cho, G Hwang and Y Shim, "Energy concentration of the focusing energy-critical fNLS", J. Math. Anal. Appl. 437 (2016), no. 1, 310-329

  21. Y Cho, G Hwang, S Kwon and S Lee, "Well-posedness and ill-posedness for the cubic fractional Schrödinger equations", DCDS-A (Vol. 35, No. 7) 2015, 2863-2880

  22. Y Cho, G Hwang, S Kwon and S Lee, "On the finite time blowup for Hartree equations", P. ROY. SOC. EDINB (145A) 2015, 467-479

  23. Y Cho, H Hajaiej, G Hwang and T Ozawa, "On the orbital stability of fractional Schrödinger equations", Commun. Pure. Appl. Anal Vol.13, No.3, 2014, 1267-1282

  24. Y Cho, G Hwang, S Kwon and S Lee, "Profile decompositions of fractional Schrödinger equations with angularly regular data", J. Differential. Equations 256 (2014), 3011-3037

  25. Y Cho, G Hwang, S Kwon and S Lee, "Profile decompositions and Blowup phenomena of mass critical fractional Schrödinger equations", Nonlinear Analysis 86 (2013), 12-29

  26. Y Cho, H Hajaiej, G Hwang and T Ozawa, "On the Cauchy problem of fractional Schrödinger equation with Hartree type nonlinearity", Funkcialaj Ekvacioj 56 (2013), 193-224

  27. Y Cho, G Hwang and T Ozawa, "Global well-posedness of critical nonlinear Schrödinger equations below $L^2$", DCDS-A (Vol. 33, No. 4) 2013, 1389-1405

  28. Y Cho, G Hwang and S Lee, "An endpoint Strichartz estimate in polar coordinates", RIMS Kokyuroku Bessatsu B33 (2012), 49-57