This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant(x,t)∈R^+×R^+,with the null-Dirichlet boundary condition or the null-Neumann bou...This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant(x,t)∈R^+×R^+,with the null-Dirichlet boundary condition or the null-Neumann boundary condition on u. We show that the corresponding initial-boundary value problem admits a unique global smooth solution which tends timeasymptotically to the nonlinear diffusion wave. Compared with the previous work about Euler equations with constant coefficient damping, studied by Nishihara and Yang(1999), and Jiang and Zhu(2009, Discrete Contin Dyn Syst), we obtain a general result when the initial perturbation belongs to the same space. In addition,our main novelty lies in the fact that the cut-off points of the convergence rates are different from our previous result about the Cauchy problem. Our proof is based on the classical energy method and the analyses of the nonlinear diffusion wave.展开更多
In this paper,the analytical blowup solutions of the N-dimensional radial symmetric compressible Euler equations are constructed.Some previous results of the blowup solutions for the compressible Euler equations with ...In this paper,the analytical blowup solutions of the N-dimensional radial symmetric compressible Euler equations are constructed.Some previous results of the blowup solutions for the compressible Euler equations with constant damping are generalized to the time-depending damping case.The generalization is untrivial because that the damp coefficient is a nonlinear function of time t.展开更多
Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory an...Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory and variational principle separately. It has two kinds of expressions including the dissipation term. Model n is based on the energy conservation equation with energy flux through the wave crest lines in orthogonal curvilinear coordinates and the wave kinematic conservation equation. The analysis and comparison and special cases of these two models are also given.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11331005,11771150,11601164 and 11601165)
文摘This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant(x,t)∈R^+×R^+,with the null-Dirichlet boundary condition or the null-Neumann boundary condition on u. We show that the corresponding initial-boundary value problem admits a unique global smooth solution which tends timeasymptotically to the nonlinear diffusion wave. Compared with the previous work about Euler equations with constant coefficient damping, studied by Nishihara and Yang(1999), and Jiang and Zhu(2009, Discrete Contin Dyn Syst), we obtain a general result when the initial perturbation belongs to the same space. In addition,our main novelty lies in the fact that the cut-off points of the convergence rates are different from our previous result about the Cauchy problem. Our proof is based on the classical energy method and the analyses of the nonlinear diffusion wave.
基金supported by the Project of Youth Backbone Teachers of Colleges and Universities in Henan Province(2019GGJS176)the Vital Science Research Foundation of Henan Province Education Department(22A110024)。
文摘In this paper,the analytical blowup solutions of the N-dimensional radial symmetric compressible Euler equations are constructed.Some previous results of the blowup solutions for the compressible Euler equations with constant damping are generalized to the time-depending damping case.The generalization is untrivial because that the damp coefficient is a nonlinear function of time t.
基金This work was financially supported by the Science Foundation of National Education Committee of China
文摘Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory and variational principle separately. It has two kinds of expressions including the dissipation term. Model n is based on the energy conservation equation with energy flux through the wave crest lines in orthogonal curvilinear coordinates and the wave kinematic conservation equation. The analysis and comparison and special cases of these two models are also given.
