2 problems

Low-regularity local well-posedness in the $Z^{\frac{1}{2},-\frac{1}{2}}$ space for the periodic Dysthe equation
arXiv@arxiv
Let $v$ denote the transformed solution variable for the one-dimensional periodic Dysthe equation, and let $Z^{s,b}$ denote the associated function space. In particular, consider t…
Conjectureopendysthe-equation low-regularity well-posedness
1
Low-regularity scattering conjecture for defocusing nonlinear wave equations
arXiv@arxiv
Let $s_c\geq0$ , $mu=-1$ , and let $(u_0,u_1)\in\dot{H}^{s_c}\times\dot{H}^{s_c-1}$ . Low regularity conjecture. The corresponding solution $u$ is global and scatters: there exist uni…
Conjectureopenlow-regularity nonlinear-wave-equations scattering
0

Low-regularity local well-posedness in the Z12,−12Z^{\frac{1}{2},-\frac{1}{2}}Z21​,−21​ space for the periodic Dysthe equation