Local and global well-posedness for the 2D Zakharov-Kuznetsov-Burgers equation in low regularity Sobolev space

In the present paper, we consider the Cauchy problem of the 2D Zakharov-Kuznetsov-Burgers (ZKB) equation, which has the dissipative term $-\partial_x^2u$. This is known that the 2D Zakharov-Kuznetsov equation is well-posed in $H^s(\mathbb{R}^2)$ for $s>1/2$, and the 2D nonlinear parabolic equation with quadratic derivative nonlinearity is well-posed in $H^s(\mathbb{R}^2)$ for $s\ge 0$. By using the Fourier restriction norm with dissipative effect, we prove the well-posedness for ZKB equation in $H^s(\mathbb{R}^2)$ for $s>-1/2$.Comment: 25 page

Well-posedness for a system of quadratic derivative nonlinear Schr\"odinger equations with low regularity periodic initial data

We consider the Cauchy problem of a system of quadratic derivative nonlinear Schr\"odinger equations which was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. For the nonperiodic case, the author proved the small data global well-posedness and the scattering at the scaling critical regularity for $d\geq 2$ when the coefficients of Laplacian satisfy some condition. In the present paper, we prove the well-posedness of the system for the periodic case. In particular, well-posedness is proved at the scaling critical regularity for $d\geq 3$ under some condition for the coefficients of Laplacian.Comment: 22 pages. arXiv admin note: text overlap with arXiv:1309.433

Glass-to-metal seals comprising relatively high expansion metals

A glass suitable for glass-to-metal seals that has a resistance to attack by moisture and a high coefficient of linear thermal expansion is introduced. Linear expansion covers the range from 12 to 14 x 10 to the minus 6 C between room temperature and 500 C. The glass is essentially composed of, by molar percent, about 9% of K2O, about 10% of Na2O, about 70% of SiO2, about 6% Al2O3, and about 5% of MgO

Classical Radiation Formula in the Rindler Frame

In a preceding paper [T. Hirayama, Prog. Theor. Phys. 106 (2001), 71], the power of the classical radiation emitted by a moving charge was evaluated in the Rindler frame. In this paper, we give a simpler derivation of this radiation formula, including an estimation of the directional dependence of the radiation. We find that the splitting of the energy-momentum tensor into a bound part I' and an emitted part II' is consistent with the three conditions introduced in the preceding paper, also for each direction within the future light cone.Comment: 11 pages, 1 figure adde