Korteweg模型中传播相界的精确稳定性判据
A sharp stability criterion for propagating phase boundaries in Korteweg's model
摘要：
最近，Benzoni--Gavage、Danchin、Descombes和Jamet根据某一“不稳定矩”关于波速的凸性，给出了相变等熵气体动力学Korteweg模型的孤波解的线性和非线性稳定性的充分条件，其等价于在运动约束的部分子集下关于相关哈密顿能量的变分稳定性;他们推测这个条件也是必要的。在这里，我们计算的埃文斯函数在原点的二阶导数的谱稳定性的一个尖锐的标准，并表明它是等价的变分条件得到的Benzoni-Gavage等人，回答他们的猜想在积极的。
英文摘要：
Recently, Benzoni--Gavage, Danchin, Descombes, and Jamet have given a sufficient condition for linear and nonlinear stability of solitary wave solutions of Korteweg's model for phase-transitional isentropic gas dynamics in terms of convexity of a certain ``moment of instability'' with respect to wave speed, which is equivalent to variational stability with respect to the associated Hamiltonian energy under a partial subset of the constraints of motion; they conjecture that this condition is also necessary. Here, we compute a sharp criterion for spectral stability in terms of the second derivative of the Evans function at the origin, and show that it is equivalent to the variational condition obtained by Benzoni--Gavage et al, answering their conjecture in the positive.
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