论文标题
加权各向异性Sobolev空间中分散概括的BO-ZK方程的持久性属性
Persistence properties for the dispersion generalized BO-ZK equation in weighted anisotropic Sobolev spaces
论文作者
论文摘要
在本文中，我们研究了与分散概括 - 苯甲酸 - Zakharov-kuznetsov方程相关的初始问题问题，$$ u_ {t}+d^{a+1} _x \ partial_ {x} _ {x} x} $$ 更具体地说，我们研究了在加权各向异性Sobolev space $ h^{（1 +a）s，2s}（\ r^{2}）\ cap l^{2}（（x^^{2r_1} +y^y^{2r_2} {2r_2}）dxdy）中，$ r的$ r，通过建立独特的延续属性，我们还表明，相对于$ x $方向的衰减，我们的结果是明显的。
In this paper we study the initial-value problem associated with the dispersion generalized-Benjamin-Ono-Zakharov-Kuznetsov equation, $$ u_{t}+D^{a+1}_x \partial_{x}u+u_{xyy}+uu_{x}=0, \qquad a\in(0,1). $$ More specifically, we study the persistence property of the solution in the weighted anisotropic Sobolev spaces $$ H^{(1+a)s,2s}(\R^{2})\cap L^{2}((x^{2r_1} +y^{2r_2})dxdy), $$ for appropriate $s$, $r_1$ and $r_2$. By establishing unique continuation properties we also show that our results are sharp with respect to the decay in the $x$-direction.
