论文标题
Schrödinger改良的Boussinesq系统在两个空间维度
Schrödinger-improved Boussinesq system in two space dimensions
论文作者
论文摘要
我们研究了二维域中施罗丁改良的Boussinesq系统的库奇问题。在对数据的自然假设下，我们证明了全球强解决方案的存在和独特性。此外，我们将全局溶液的“改进”极限视为离子声波方程中最高级线性项的系数往往为零。在数据上与Zakharov情况相同的小假设下，“改进”极限中的解决方案显示出满足Zakharov系统的满足。
We study the Cauchy problem for the Schrödinger-improved Boussinesq system in a two dimensional domain. Under natural assumptions on the data without smallness, we prove the existence and uniqueness of global strong solutions. Moreover, we consider the vanishing "improvement" limit of global solutions as the coefficient of the linear term of the highest order in the equation of ion sound waves tends to zero. Under the same smallness assumption on the data as in the Zakharov case, solutions in the vanishing "improvement" limit are shown to satisfy the Zakharov system.
