Abstract. The three-dimensional equations of compressible magnetohydrodynamic isentropic flows are considered. An initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of global weak solutions are established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent γ > 3 2 and constant viscosity coefficients.

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Increasing evidence indicates that brown adipose tissue (BAT) transplantation enhances whole-body energy metabolism in a mouse model of diet-induced obesity. However, it remains unclear whether BAT also has such beneficial effects on genetically obese mice. To address this issue, we transplanted BAT from C57/BL6 mice into the dorsal subcutaneous region of age- and sex-matched leptin deficient Ob/Ob mice. Interestingly, BAT transplantation led to a significant reduction of body weight gain with increased oxygen consumption and decreased total body fat mass, resulting in improvement of insulin resistance and liver steatosis. In addition, BAT transplantation increased the level of circulating adiponectin, whereas it reduced the levels of circulating free T3 and T4, which regulate thyroid hormone sensitivity in peripheral tissues. BAT transplantation also increased β3-adrenergic receptor and fatty acid oxidation related gene expression in subcutaneous and epididymal (EP) white adipose tissue. Accordingly, BAT transplantation increased whole-body thermogenesis. Taken together our results demonstrate that BAT transplantation may reduce obesity and its related diseases by activating endogenous BAT.

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A free boundary problem for nonlinear magnetohydrodynamics with general large initial data is investigated. The existence, uniqueness, and regularity of global solutions are established with large initial data in H 1 : It is shown that neither shock waves nor vacuum and concentration in the solutions are developed in a finite time, although there is a complex interaction between the hydrodynamic and magnetodynamic effects. An existence theorem of global solutions with large discontinuous initial data is also established. # 2002 Elsevier Science (USA)

The equations of the three-dimensional viscous, compressible, and heat conducting magnetohydrodynamic flows are considered in a bounded domain. The viscosity coefficients and heat conductivity can depend on the temperature. A solution to the initial-boundary value problem is constructed through an approximation scheme and a weak convergence method. The existence of a global variational weak solution to the three-dimensional full magnetohydrodynamic equations with large data is established.1991 Mathematics Subject Classification. 35Q36, 35D05, 76W05.

Determining the Equation of State (EOS) of dense neutron-rich nuclear matter is a shared goal of both nuclear physics and astrophysics. Except possible phase transitions, the density dependence of nuclear symmetry Esym(ρ) is the most uncertain part of the EOS of neutron-rich nucleonic matter especially at supra-saturation densities. Much progresses have been made in recent years in predicting the symmetry energy and understanding why it is still very uncertain using various microscopic nuclear many-body theories and phenomenological models. Simultaneously, significant progresses have also been made in probing the symmetry energy in both terrestrial nuclear laboratories and astrophysical observatories. In light of the GW170817 event as well as ongoing or planned nuclear experiments and astrophysical observations probing the EOS of dense neutron-rich matter, we review recent progresses and identify new challenges to the best knowledge we have on several selected topics critical for understanding astrophysical effects of the nuclear symmetry energy.PACS. 2 6.60.Kp Contents B.A Li, P.G. Krastev, D.H. Wen and N.B. Zhang: Astrophysical Effects of Nuclear Symmetry Energy 5.2.2 Predicted correlation strength between the radii of neutron stars and the symmetry energy from low to high densities 32 5.2.3 Predicted effects of the symmetry energy on the tidal deformability of neutron stars 33 5.3 Post-GW170817 analyses of tidal deformability and radii of neutron stars as well as constraints on the nuclear EOS and symmetry energy . . . 34 5.3.

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