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Diophantine conditions in well-posedness theory for a coupled modulated Korteweg-de Vries system
Thomas Arthur, Damiano Greco, Kotaro Tsugawa
The paper investigates global well‑posedness for a coupled, time‑modulated Korteweg‑de Vries system on the circle, using Diophantine conditions to control resonances when the coupl…
Refined global well-posedness for the periodic modulated Korteweg-de Vries equation
Damiano Greco, Massimiliano Gubinelli, Shao Liu +1
We revisit the pathwise global well-posedness issue of the modulated Korteweg-de Vries equation (KdV) on the circle. In the previous work (2024), by combining the -method and th…
Unconditional well-posedness of the stochastic Korteweg-de Vries equation on the real line
Damiano Greco, Tadahiro Oh, Kotaro Tsugawa
We study well-posedness issues of the stochastic Korteweg-de Vries equation (SKdV) with an additive noise, posed on the real line. By using the Fourier restriction norm method adap…
Elementary Brezis-Browder type results and Representation formulae for s-harmonic functions
Damiano Greco
We prove Brezis--Browder type results for fractional Sobolev spaces and quantitative type estimates for -harmonic functions. Furthermore, we give sufficient conditions for distr…
Optimal decay and regularity for a Thomas--Fermi type variational problem
Damiano Greco
We study existence and qualitative properties of the minimizers for a Thomas--Fermi type energy functional defined by $$E_α(Ï):=\frac{1}{q}\int_{\mathbb{R}^d}|Ï(x)|^q dx+\frac{1…
Ground states of a nonlocal variational problem and Thomas-Fermi limit for the Choquard equation
Damiano Greco, Yanghong Huang, Zeng Liu +1
We study nonnegative optimizers of a Gagliardo-Nirenberg type inequality $$\iint_{\mathbb{R}^N \times \mathbb{R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-α}} dx\, dy\le C\Big(\int_…