Zobrazeno 1 - 10
of 133
pro vyhledávání: '"Hunter, John K."'
This paper proves that the motion of small-slope vorticity fronts in the two-dimensional incompressible Euler equations is approximated on cubically nonlinear timescales by a Burgers-Hilbert equation derived by Biello and Hunter (2010) using formal a
Externí odkaz:
http://arxiv.org/abs/2006.08163
We prove the global existence of solutions with small and smooth initial data of a nonlinear dispersive equation for the motion of generalized surface quasi-geostrophic (GSQG) fronts in a parameter regime $1<\alpha<2$, where $\alpha=1$ corresponds to
Externí odkaz:
http://arxiv.org/abs/2005.09154
We use contour dynamics to derive equations of motion for infinite planar surface quasi-geostrophic (SQG) fronts, and show that it leads to the same result as a regularization procedure introduced previously by Hunter and Shu (2018).
Comment: 12
Comment: 12
Externí odkaz:
http://arxiv.org/abs/1907.06593
The generalized surface quasi-geostrophic (GSQG) equations are transport equations for an active scalar that depend on a parameter $0<\alpha \le 2$. Special cases are the two-dimensional incompressible Euler equations ($\alpha = 2$) and the surface q
Externí odkaz:
http://arxiv.org/abs/1904.13380
Autor:
Hunter, John K., Smothers, Evan B.
We derive a degenerate quasilinear Schr\"odinger equation that describes the resonant reflection of very weak, nonlinear sound waves off a weak sawtooth entropy wave.
Externí odkaz:
http://arxiv.org/abs/1810.11913
Publikováno v:
Pure Appl. Analysis 3 (2021) 403-472
We consider a nonlinear, spatially-nonlocal initial value problem in one space dimension on $\mathbb{R}$ that describes the motion of surface quasi-geostrophic (SQG) fronts. We prove that the initial value problem has a unique local smooth solution u
Externí odkaz:
http://arxiv.org/abs/1808.07631
We prove local well-posedness in the Sobolev spaces $\dot H^s(\mathbb{T})$, with $s>7/2$, for an initial value problem for a nonlocal, cubically nonlinear, dispersive equation that provides an approximate description of the evolution of surface quasi
Externí odkaz:
http://arxiv.org/abs/1801.02718
Autor:
Hunter, John K., Shu, Jingyang
We derive regularized contour dynamics equations for the motion of infinite sharp fronts in the two-dimensional incompressible Euler, surface quasi-geostrophic (SQG), and generalized surface quasi-geostrophic (gSQG) equations. We derive a cubic appro
Externí odkaz:
http://arxiv.org/abs/1709.03194
Publikováno v:
Discrete & Continuous Dynamical Systems: Series A; Sep2024, Vol. 44 Issue 9, p1-43, 43p
Autor:
Halabi, Ryan G., Hunter, John K.
We derive an asymptotic equation for quasi-static, nonlinear surface plasmons propagating on a planar interface between isotropic media. The plasmons are nondispersive with a constant linearized frequency that is independent of their wavenumber. The
Externí odkaz:
http://arxiv.org/abs/1510.08188