Uniqueness results for Zakharov-Kuznetsov equation
نویسندگان
چکیده
منابع مشابه
Well-posedness results for the 3D Zakharov-Kuznetsov equation
We prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov equation ∂tu+∆∂xu+u∂xu = 0 in the Sobolev spaces Hs(R3), s > 1, as well as in the Besov space B 2 (R 3). The proof is based on a sharp maximal function estimate in time-weighted spaces.
متن کاملExact Travelling Wave Solutions for a Modified Zakharov–Kuznetsov Equation
The modied Zakharov–Kuznetsov (mZK) equation, ut + uux + uxxx + uxyy = 0, (1) represents an anisotropic two-dimensional generalization of the Korteweg–de Vries equation and can be derived in a magnetized plasma for small amplitude Alfvén waves at a critical angle to the undisturbed magnetic field, and has been studied by many authors because of its importance [1–5]. However, Eq. (1) possesses m...
متن کاملWell-posedness for the 2d Modified Zakharov-kuznetsov Equation
We prove that the initial value problem for the two-dimensional modified ZakharovKuznetsov equation is locally well-posed for data in H(R), s > 3/4. Even though the critical space for this equation is L(R) we prove that well-posedness is not possible in such space. Global well-posedness and a sharp maximal function estimate are also established.
متن کاملLocal and global well-posedness results for the Benjamin-Ono-Zakharov-Kuznetsov equation
We show that the initial value problem associated to the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov equation ut −D α xux + uxyy = uux, (t, x, y) ∈ R , 1 ≤ α ≤ 2, is locally well-posed in the spaces Es, s > 2 α − 3 4 , endowed with the norm ‖f‖Es = ‖〈|ξ| α + μ〉f̂‖L2(R2). As a consequence, we get the global wellposedness in the energy space E1/2 as soon as α > 8 5 . The proof is based ...
متن کاملApproximate analytical solution to a time-fractional Zakharov-Kuznetsov equation
In this paper we present approximate analytical solution of a time-fractional Zakharov-Kuznetsov equation via the fractional iteration method. The fractional derivatives are described in the Caputo sense. The approximate results show that the fractional iteration method is a very efficient technique to handle fractional partial differential equations.
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: Communications in Partial Differential Equations
سال: 2019
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605302.2019.1581803