CAJ | 학술논문

本文研究三维空间中一个具有阻尼项的推广的Zakharov系统的亚音速极限,给出从Zakharov到非线性Schr(o)dinger方程形式极限的严格数学证明.利用弱紧性讨论和能量方法建立了弱收敛和强收敛结果.此外,还需指出,频率分解技术和Strichartz估计对强收敛性的证明是非常有用的.
본문연구삼유공간중일개구유조니항적추엄적Zakharov계통적아음속겁한,급출종Zakharov도비선성Schr(o)dinger방정형식겁한적엄격수학증명.이용약긴성토론화능량방법건립료약수렴화강수렴결과.차외,환수지출,빈솔분해기술화Strichartz고계대강수렴성적증명시비상유용적.
This paper is concerned with the subsonic limit of a generalized Zakharov system(GZS)in three space dimensions without or with a damping term.Rigorous mathematical justification in the formal limit from the solution of GZS to the one of nonlinear Schr(o)dinger(NLS) equation is provided.Weak and strong convergence results are established by using the weak compactness argument and the energy method,respectively.On the other hand,frequency splitting and Strichartz estimates are available to prove the strong convergence.