Recently,the global existence of weak solutions to the compressible Navier-Stokes equations with vacuum has attracted much attention.In this paper,we study the one-dimension isentropic Navier-Stokes equations with gra...Recently,the global existence of weak solutions to the compressible Navier-Stokes equations with vacuum has attracted much attention.In this paper,we study the one-dimension isentropic Navier-Stokes equations with gravitational force and fixed boundary condition when the density connects with vacuum discontinuously.We prove the global existence and the uniqueness of weak solution,requiring less regularity of the initial data.展开更多
In this paper, we investigate the coupled viscous quantum magnetohydrodynamic equations and nematic liquid crystal equations which describe the motion of the nematic liquid crystals under the magnetic field and the qu...In this paper, we investigate the coupled viscous quantum magnetohydrodynamic equations and nematic liquid crystal equations which describe the motion of the nematic liquid crystals under the magnetic field and the quantum effects in the two-dimensional case. We prove the existence of the global finite energy weak solutions by use of a singular pressure close to vacuum. Then we obtain the local-in-time existence of the smooth solution. In the final, the blow-up of the smooth solutions is studied. The main techniques are Faedo-Galerkin method, compactness theory, Arzela-Ascoli theorem and construction of the functional differential inequality.展开更多
The existence of global weak solutions for a generalized Benjamin-Bona-MahonyBurgers equation is established in the space C（[0, ∞） × R） ∩ L~∞（[0, ∞）; H1（R）） under the condition that its initial value ...The existence of global weak solutions for a generalized Benjamin-Bona-MahonyBurgers equation is established in the space C（[0, ∞） × R） ∩ L~∞（[0, ∞）; H1（R）） under the condition that its initial value belongs to the space H1（R）. A one-sided super bound estimate and a space-time higher-norm estimate on the first order derivatives of the solution with respect to the space variable are derived to prove the existence.展开更多
In this paper, we deal with the generalized derivative Ginzburg-Landau equation in two spatial dimensions, and obtain the existence of global weak solutions for this equation subject to periodic boundary conditions.
文摘Recently,the global existence of weak solutions to the compressible Navier-Stokes equations with vacuum has attracted much attention.In this paper,we study the one-dimension isentropic Navier-Stokes equations with gravitational force and fixed boundary condition when the density connects with vacuum discontinuously.We prove the global existence and the uniqueness of weak solution,requiring less regularity of the initial data.
基金supported by the Foundation of Guangzhou University (Grant No. 2700050357)National Natural Science Foundation of China (Grant No. 11731014)
文摘In this paper, we investigate the coupled viscous quantum magnetohydrodynamic equations and nematic liquid crystal equations which describe the motion of the nematic liquid crystals under the magnetic field and the quantum effects in the two-dimensional case. We prove the existence of the global finite energy weak solutions by use of a singular pressure close to vacuum. Then we obtain the local-in-time existence of the smooth solution. In the final, the blow-up of the smooth solutions is studied. The main techniques are Faedo-Galerkin method, compactness theory, Arzela-Ascoli theorem and construction of the functional differential inequality.
文摘The existence of global weak solutions for a generalized Benjamin-Bona-MahonyBurgers equation is established in the space C（[0, ∞） × R） ∩ L~∞（[0, ∞）; H1（R）） under the condition that its initial value belongs to the space H1（R）. A one-sided super bound estimate and a space-time higher-norm estimate on the first order derivatives of the solution with respect to the space variable are derived to prove the existence.
基金This work is supported by the Postdoctoral Foundation of China.
文摘In this paper, we deal with the generalized derivative Ginzburg-Landau equation in two spatial dimensions, and obtain the existence of global weak solutions for this equation subject to periodic boundary conditions.
