منابع مشابه
The Existence of Strong Solutions to the 3d Zakharov-kuznestov Equation in a Bounded Domain
We consider the Zakharov-Kuznestov (ZK) equation posed in a limited domain M = (0, 1)x × (−π/2, π/2)d, d = 1, 2 supplemented with suitable boundary conditions. We prove that there exists a solution u ∈ C([0, T ];H1(M)) to the initial and boundary value problem for the ZK equation in both dimensions 2 and 3 for every T > 0. To the best of our knowledge, this is the first result of the global exi...
متن کاملQuantum Zakharov Equations
In this paper we investigate the existence of soliton solutions for a modified form of the Zakharov equations describing modulational instabilities in quantum plasmas. In particular, we show that quantum effects suppress the easily identifiable soliton solutions, obtained in the adiabatic limit. In this limit, the quantum Zakharov equations become a coupled fourth order system, not amenable to ...
متن کاملEXISTENCE OF A STEADY FLOW WITH A BOUNDED VORTEX IN AN UNBOUNDED DOMAIN
We prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. The data prescribed is the rearrangement class of the vorticity field. The corresponding stream function satisfies a semilinear elliptic partial differential equation. The result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...
متن کاملVariational approach for the quantum Zakharov system
The quantum Zakharov system is described in terms of a Lagrangian formalism. A time-dependent Gaussian trial function approach for the envelope electric field and the low-frequency part of the density fluctuation leads to a coupled, nonlinear system of ordinary differential equations. In the semiclassic case, linear stability analysis of this dynamical system shows a destabilizing rôle played b...
متن کاملexistence of a steady flow with a bounded vortex in an unbounded domain
we prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. the data prescribed is the rearrangement class of the vorticity field. the corresponding stream function satisfies a semilinear elliptic partial differential equation. the result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...
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ژورنال
عنوان ژورنال: Zeitschrift für angewandte Mathematik und Physik
سال: 2012
ISSN: 0044-2275,1420-9039
DOI: 10.1007/s00033-012-0278-9