Weak solutions of the three-dimensional vorticity equation with vortex singularities
نویسندگان
چکیده
منابع مشابه
On the Motion of Vortex Sheets with Surface Tension in Three-Dimensional Euler Equations with Vorticity
The motion of vortex sheets with surface tension has been analyzed in the setting of irrotational flows by Ambrose [1] and Ambrose and Masmoudi [2] in two dimensions, and by Ambrose and Masmoudi [3] in three dimensions. With irrotationality, the nonlinear Euler equations reduce to Poisson’s equation for the pressure function in the bulk, and the motion of the vortex sheet is decoupled from that...
متن کاملPeriodic Solutions of Liénard Equation with One or Two Weak Singularities
In this paper we study the existence and asymptotic stability of periodic solutions of the differential equation ẍ+ f (x)ẋ+g(x) = h(t), where h(t) is T -periodic, f (x) is positive and g(x) is strictly monotonically increasing and has one or two weak singularities. The method of proof relies on the construction of a positively invariant region of the flux. Mathematics subject classification (20...
متن کاملVortex solutions of the Liouville equation
The most general vortex solution of the Liouville equation (which arises in nonrelativistic Chern-Simons theory) is associated with rational functions, f(z) = P (z)/Q(z) where P (z) and Q(z) are both polynomials, degP < degQ ≡ N . This allows us to prove that the solution depends on 4N parameters without the use of an index theorem, as well as the flux quantization : Φ = −4Nπ(sign κ).
متن کاملTwo soliton solutions to the three dimensional gravitational Hartree equation
We construct non dispersive two soliton solutions to the three dimensional gravitational Hartree equation whose trajectories asymptotically reproduce the nontrapped dynamics of the gravitational two body problem.
متن کاملGlobal stability of vortex solutions of the two-dimensional Navier-Stokes equation
Both experimental and numerical studies of fluid motion indicate that initially localized regions of vorticity tend to evolve into isolated vortices and that these vortices then serve as organizing centers for the flow. In this paper we prove that in two dimensions localized regions of vorticity do evolve toward a vortex. More precisely we prove that any solution of the two-dimensional Navier-S...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physics of Fluids
سال: 1988
ISSN: 0031-9171
DOI: 10.1063/1.866680