Search Results - "Kwon, Soonsik"

On the fifth-order KdV equation: Local well-posedness and lack of uniform continuity of the solution map by Kwon, Soonsik

“…In this paper we prove that the following fifth-order equation arising from the KdV hierarchy { ∂ t u + ∂ x 5 u + c 1 ∂ x u ∂ x 2 u + c 2 u ∂ x 3 u = 0 , u : R…”
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The modified scattering of two dimensional semi-relativistic Hartree equations by Kwon, Soonsik, Lee, Kiyeon, Yang, Changhun

“…In this paper, we consider the asymptotic behaviors of small solutions to the semi-relativistic Hartree equations in two dimension. The nonlinear term is the…”
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Orbital stability of solitary waves for derivative nonlinear Schrödinger equation by Kwon, Soonsik, Wu, Yifei

“…In this paper, we show the orbital stability of solitons arising in the cubic derivative nonlinear Schrödinger equations. We consider the zero mass case that…”
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Poincaré-Dulac Normal Form Reduction for Unconditional Well-Posedness of the Periodic Cubic NLS by Guo, Zihua, Kwon, Soonsik, Oh, Tadahiro

“…We implement an infinite iteration scheme of Poincaré-Dulac normal form reductions to establish an energy estimate on the one-dimensional cubic nonlinear…”
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Profile decompositions and blowup phenomena of mass critical fractional Schrödinger equations by Cho, Yonggeun, Hwang, Gyeongha, Kwon, Soonsik, Lee, Sanghyuk

“…We study, under the radial symmetry assumption, the solutions to the fractional Schrödinger equations of critical nonlinearity in R1+d,d≥2, with Lévy index…”
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On Unconditional Well-Posedness of Modified KdV by Kwon, Soonsik, Oh, Tadahiro

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Well-posedness and ill-posedness of the fifth-order modified KdV equation by Soonsik Kwon

“…We consider the initial value problem of the fifth-order modified KdV equation on the Sobolev spaces. $$displaylines{ partial_t u - partial_x^5u +…”
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Nonexistence of soliton-like solutions for defocusing generalized KdV equations by Soonsik Kwon, Shuanglin Shao

“…We consider the global dynamics of the defocusing generalized KdV equation $$ \partial_t u + \partial_x^3 u = \partial_x(|u|^{p-1}u). $$ We use Tao's theorem…”
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Critical local well-posedness of the nonlinear Schrödinger equation on the torus by Kwak, Beomjong, Kwon, Soonsik

“…In this paper, we study the local well-posedness of nonlinear Schrödinger equations on tori \mathbb{T}^{d} at the critical regularity. We focus on cases where…”
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Construction of Blow-Up Manifolds to the Equivariant Self-dual Chern–Simons–Schrödinger Equation by Kim, Kihyun, Kwon, Soonsik

“…We consider the self-dual Chern–Simons–Schrödinger equation (CSS) under equivariance symmetry. Among others, (CSS) has a static solution Q and the…”
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Rough solutions of the fifth-order KdV equations by Guo, Zihua, Kwak, Chulkwang, Kwon, Soonsik

“…We consider the Cauchy problem of the fifth-order equation arising from the Korteweg–de Vries (KdV)…”
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A remark on normal forms and the “upside-down” I-method for periodic NLS: Growth of higher Sobolev norms by Colliander, James, Kwon, Soonsik, Oh, Tadahiro

“…We study growth of higher Sobolev norms of solutions of the onedimensional periodic nonlinear Schrödinger equation (NLS). By a combination of the normal form…”
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Profile decompositions of fractional Schrödinger equations with angularly regular data by Cho, Yonggeun, Hwang, Gyeongha, Kwon, Soonsik, Lee, Sanghyuk

“…We study the fractional Schrödinger equations in R1+d, d⩾3, of order d/(d−1)<α<2. Under the angular regularity assumption we prove linear and nonlinear profile…”
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Critical local well-posedness of the nonlinear Schr\"odinger equation on the torus by Kwak, Beomjong, Kwon, Soonsik

“…In this paper, we study the local well-posedness of nonlinear Schr\"odinger equations on tori $\mathbb{T}^{d}$ at the critical regularity. We focus on cases…”
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Soliton resolution for Calogero--Moser derivative nonlinear Schr\"odinger equation by Kim, Taegyu, Kwon, Soonsik

“…We consider soliton resolution for the Calogero--Moser derivative nonlinear Schr\"odinger equation (CM-DNLS). A rigorous PDE analysis of (CM-DNLS) was recently…”
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Blow-up dynamics for radial self-dual Chern-Simons-Schr\"odinger equation with prescribed asymptotic profile by Kim, Kihyun, Kwon, Soonsik, Oh, Sung-Jin

“…We construct finite energy blow-up solutions for the radial self-dual Chern-Simons-Schr\"odinger equation with a continuum of blow-up rates. Our result stands…”
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Construction of smooth chiral finite-time blow-up solutions to Calogero--Moser derivative nonlinear Schr\"odinger equation by Kim, Kihyun, Kim, Taegyu, Kwon, Soonsik

“…We consider the Calogero--Moser derivative nonlinear Schr\"odinger equation (CM-DNLS), which is an $L^{2}$-critical nonlinear Schr\"odinger equation with…”
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Construction of blow-up manifolds to the equivariant self-dual Chern-Simons-Schr\"odinger equation by Kim, Kihyun, Kwon, Soonsik

“…Ann. PDE 9 (2023), no. 1, Paper No. 6, 129 pp We consider the self-dual Chern-Simons-Schr\"odinger equation (CSS) under equivariance symmetry. Among others,…”
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The modified scattering of 2 dimensional semi-relativistic Hartree equations by Kwon, Soonsik, Lee, Kiyeon, Yang, Changhun

“…In this paper, we consider the asymptotic behaviors of small solutions to the semi-relativistic Hartree equations in two dimension. The nonlinear term is…”
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On pseudoconformal blow-up solutions to the self-dual Chern-Simons-Schr\"odinger equation: existence, uniqueness, and instability by Kim, Kihyun, Kwon, Soonsik

“…Mem. Amer. Math. Soc. 284 (2023), no. 1409, v+128 pp We consider the self-dual Chern-Simons-Schr\"odinger equation (CSS). CSS is $L^{2}$-critical, admits…”
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