In this note, we prove that the Schrodinger flow of maps from a closed Rieman surface into a compact irreducible Hermitian symmetric space admits a global weak solution. Also, we show the existence of weak solutions t...In this note, we prove that the Schrodinger flow of maps from a closed Rieman surface into a compact irreducible Hermitian symmetric space admits a global weak solution. Also, we show the existence of weak solutions to the initial value problem of Heisenberg model wit Lie algebra values, which is closely related to the Schrodinger flow on compact Hermitian symmetric spaces.展开更多
The authors give a proof of the convergence of the solution of the parabolic approximation towards the entropic solution of the scalar conservation law div f(x, t, u) = 0 in several space dimensions. For any initial c...The authors give a proof of the convergence of the solution of the parabolic approximation towards the entropic solution of the scalar conservation law div f(x, t, u) = 0 in several space dimensions. For any initial condition uo (RN) and for alarge class of flux f, they also prove the strong converge in any space, using the notion ofentropy process solution, which is a generalization of the measure-valued solutions of Diperna.展开更多
文摘In this note, we prove that the Schrodinger flow of maps from a closed Rieman surface into a compact irreducible Hermitian symmetric space admits a global weak solution. Also, we show the existence of weak solutions to the initial value problem of Heisenberg model wit Lie algebra values, which is closely related to the Schrodinger flow on compact Hermitian symmetric spaces.
文摘The authors give a proof of the convergence of the solution of the parabolic approximation towards the entropic solution of the scalar conservation law div f(x, t, u) = 0 in several space dimensions. For any initial condition uo (RN) and for alarge class of flux f, they also prove the strong converge in any space, using the notion ofentropy process solution, which is a generalization of the measure-valued solutions of Diperna.
