Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces

The local well-posedness and low Mach number limit are considered for the multi-dimensional isentropic compressible viscous magnetohydrodynamic equations in critical spaces. First the local well-posedness of solution to the viscous magnetohydrodynamic equations with large initial data is established. Then the low Mach number limit is studied for general large data and it is proved that the solution of the compressible magnetohydrodynamic equations converges to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero. Moreover, the convergence rates are obtained.Comment: 37page

A Foreword from the Editor-in-Chief

Accompanying the development of petrochemical industry, great progress has been achieved in the organic polymer materials. It is well known that the conventional polymer materials usually consist of organosilicon polymers, polycarbonates, polyethylene, polyamide, polyurethane, polysulfone, phenolic resin and so on. Although their synthesis and applications have been well developed, the further research on them still has great significance. Moreover, natural polymers such as polysaccharides, tannins, cellulose also occupy an important position in the family of the organic polymer materials

RELATIONSHIP BETWEEN ADOLESCENT DEPRESSION AND INSECURE ATTACHMENT: MEDIATING EFFECT OF PSYCHOLOGICAL CAPITAL

Background: Depression is the primary factor influencing the mental health of adolescents. To explore the psychogenesis mechanism of adolescent depression, the relationships of adolescent depression with insecure attachment and psychological capital were discussed. Subjects and methods: A total of 200 depression patients were selected as the research group through the simple sampling method from the adolescents accepting psychological counseling in Wuhan, China, from April to June 2020, and another 200 mentally healthy adolescents were taken as the control group. Positive Psycap Questionnaire (PPQ), Center Epidemiological Studies of Depression (CES-D) scale, and Experiences in Close Relationship (ECR) scale were distributed in the two groups to evaluate their psychological capital, depression, and insecure attachment. Results: Compared with the control group, the avoidant attachment and anxious attachment scores are higher in the research group, but the score of each dimension of psychological capital and the total score is lower (P<0.05). Avoidant attachment is positively correlated with both anxious attachment and depression and negatively correlated with psychological capital. Anxious attachment shows a positive correlation with depression and a negative correlation with psychological capital. A negative correlation is observed between psychological capital and depression (P<0.05). Incomplete family, left-behind children, psychological capital, each dimension of psychological capital, avoidance attachment and anxious attachment are all independent influencing factors of adolescent depression, among which anxious attachment and avoidant attachment exert significant direct effects on adolescent depression, and psychological capital plays an incomplete mediating role in the relationships of anxious attachment and avoidant attachment with adolescent depression. Conclusion: Psychological capital can relieve the depression degree, while insecure attachment has a positive predicting effect on adolescent depression, and psychological capital exerts an incomplete mediating effect on the relationship between insecure attachment and adolescent depression