广义Davey——Stewartson系统驻波的强不稳定性
Instability for the Standing Wave of Generalized Davey-Stewartson Equation
本文研究方程驻波的强不稳定性iut+Δu+a|u|p-1u+E1(|u|2)u=0,t≥0,x∈Rn,其中a > 0,1 < p <(n-2)/((n+2)+),n∈{2,3}.当1+4/n ≤ p <(n-2)/((n+2)+)时,文[Sharp threshold of global existence and instability of standing wave for a Davey-Stewartson system,Commun.Math.Phys.,2008,283:93-125]在驻波的频率满足一定假设条件下,证明了此方程驻波的强不稳定性.本文去掉这个假设,得到相同的结论.
The aim of this paper is to study the standing wave of the generalized Davey-Stewartson equation iut+Δu+a|u|p-1u+E1(|u|2)u=0, t ≥ 0,x∈Rn, where a,b > 0, 1 < p < (n-2)/((n+2)+), n∈{2,3}. When 1+4/n ≤ p < (n-2)/((n+2)+),[Sharp threshold of global existence and instability of standing wave for a Davey-Stewartson system, Commun. Math. Phys., 2008, 283:93-125], under an assumption about the frequency of the standing wave, obtained the strongly instability of the ground state standing waves. In the present paper, We establish the same conclusion without that assumption.
Davey-Stewartson系统 / 驻波 / 强不稳定 {{custom_keyword}} /
Davey-Stewartson equation / standing wave / instability {{custom_keyword}} /
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国家自然科学基金资助项目(11371267,11771314);教育部科学技术研究重点项目(211162);四川省青年基金资助项目(2012JQ0011)
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