We consider the Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model.The model is described by a coupled system consisting of a heat equation and a quasilinear wave equation.In this paper,we w...We consider the Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model.The model is described by a coupled system consisting of a heat equation and a quasilinear wave equation.In this paper,we will construct an example with a finite time cusp singularity due to the quasilinearity of the wave equation,extended from an earlier resultonaspecial case.展开更多
In this paper, we study the existence and regularity of a solution to the initial datum problem of a semilinear generalized Tricomi equation in mixed-type initial datum on the degenerate plane is smooth away from the ...In this paper, we study the existence and regularity of a solution to the initial datum problem of a semilinear generalized Tricomi equation in mixed-type initial datum on the degenerate plane is smooth away from the origin, domain. We suppose that an and has a conormal singularity at this point, then we show that in some mixed-type domain, the solution exists and is conormal with respect to the characteristic conic surface which is issued from the origin and has a cusp singularity.展开更多
文摘We consider the Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model.The model is described by a coupled system consisting of a heat equation and a quasilinear wave equation.In this paper,we will construct an example with a finite time cusp singularity due to the quasilinearity of the wave equation,extended from an earlier resultonaspecial case.
基金Supported by National Natural Science Foundation of China (Grant No. 10871096)
文摘In this paper, we study the existence and regularity of a solution to the initial datum problem of a semilinear generalized Tricomi equation in mixed-type initial datum on the degenerate plane is smooth away from the origin, domain. We suppose that an and has a conormal singularity at this point, then we show that in some mixed-type domain, the solution exists and is conormal with respect to the characteristic conic surface which is issued from the origin and has a cusp singularity.
