WebWe study the Cauchy problem for the Zakharov system in a two dimensional domain. Under natural assumptions on the data, we prove the existence and uniqueness of global solutions in H 2 ⊕H 1.The method of the construction of global solutions depends on the proof that solutions of some regularized system form a bounded sequence in H 2 ⊕H 1 … WebContact & Support. Business Office 905 W. Main Street Suite 18B Durham, NC 27701 USA. Help Contact Us
Local Well-Posedness of the KdV Equation with Quasi-Periodic …
WebIn this research paper, we are mainly interested in the Cauchy problem for the so-called Rotational-Modified Benjamin equation. This equation was introduced to describe the … Web28 de fev. de 2024 · Published: June 2024. Abstract. We prove that the Cauchy problem for the two-dimensional Zakharov system is locally well-posed for initial data which are localized perturbations of a line solitary wave. Furthermore, for this Zakharov system, we prove a weak convergence to a nonlinear Schrödinger equation. Keywords: iron within 40k free
Cauchy Problem for the Rotational-Modified Benjamin Equation
Web23 de mai. de 2012 · We consider in this paper the rigorous justification of the Zakharov-Kuznetsov equation from the Euler-Poisson system for uniformly magnetized plasmas. We first provide a proof of the local well-posedness of the Cauchy problem for the aforementioned system in dimensions two and three. Then we prove that the long-wave … Web9 de jun. de 2013 · We prove global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in 3 space dimensions. The wave component is shown to decay pointwise at the optimal rate of t −1, whereas the Schrödinger component decays almost at a rate of t −7/6. Web3 de abr. de 2009 · We prove local in time well-posedness for the Zakharov system in two space dimensions with large initial data in L 2 × H −1/2 × H −3/2.This is the space of optimal regularity in the sense that the data-to-solution map fails to be smooth at the origin for any rougher pair of spaces in the L 2-based Sobolev scale.Moreover, it is a natural space for … port tack boat