This paper studies the existence and long time behavior of the solutions to the coupled Burgers-complex Ginzburg-Landau （Burgers-CGL） equations, which are derived from the nonlinear evolution of the coupled long-sca...This paper studies the existence and long time behavior of the solutions to the coupled Burgers-complex Ginzburg-Landau （Burgers-CGL） equations, which are derived from the nonlinear evolution of the coupled long-scale oscillatory and monotonic instabilities of a uniformly propagating combustion wave governed by a sequential chem- ical reaction, having two flame fronts corresponding to two reaction zones with a finite separation distance between them. This paper firstly shows the existence of the global solutions to these coupled equations via subtle transforms, delicate a priori estimates and a so-called continuity method, then prove the existence of the global attractor and establish the estimates of the upper bounds of Hausdorff and fractal dimensions for the attractor.展开更多
复Ginzburg-Landau (CGL)方程作为非平衡系统动力学的普适模型, 在量子流体动力学、 超导 理论及Bose-Einstein疑聚体等物理系统中具有重要应用, 适定性与渐近极限是其数学理论研究中 的重要方向。 本文针对具有混合耗散算子的CGL方程...复Ginzburg-Landau (CGL)方程作为非平衡系统动力学的普适模型, 在量子流体动力学、 超导 理论及Bose-Einstein疑聚体等物理系统中具有重要应用, 适定性与渐近极限是其数学理论研究中 的重要方向。 本文针对具有混合耗散算子的CGL方程展开系统性研究。 通过混合耗散算子的正则 性分析与特定参数比率约束条件的构造, 确立L2解的唯一性, 井借助与耗散参数相关的截断函数及 能量估计方法, 揭示了耗散系数趋于0时, 从CGL方程到高阶非线性Schro¨dinger (NLS)方程的无 粘极限及其收敛速率。The complex Ginzburg-Landau (CGL) equation, as a universal model for non-equilibrium system dynamics, has important applications in physical systems such as quantum fluid dynamics, superconductivity theory, and Bose-Einstein condensates. Well-posedness and asymptotic limit are important directions in the study of mathematical theory.This article conducts a systematic study on the CGL equation with mixed dissipa- tive operators. By analyzing the regularity of the mixed dissipation operators and constructing specific parameter ratio constraints, the uniqueness of the L2 solution is established. With the help of truncation function and energy estimates related to dissipation parameters, the inviscid limit and convergence rate from CGL equation to high-order nonlinear Schro¨dinger (NLS) equation are obtained when the dissipation coefficients approaches to 0.展开更多
In this paper, we are concerned with the existence and uniqueness of global solutions of the modified KS-CGL equations for flames governed by a sequential reaction, where the term ｜P｜2σP is replaced with the genera...In this paper, we are concerned with the existence and uniqueness of global solutions of the modified KS-CGL equations for flames governed by a sequential reaction, where the term ｜P｜2σP is replaced with the generalized form ｜P｜2P, see [18]. The main novelty compared with [18] in this paper is to control the norms of the first order of the solutions and extend the global well-posedness to three dimensional space.展开更多
基金supported by the National Natural Science Foundation of China(No.11271141)
文摘This paper studies the existence and long time behavior of the solutions to the coupled Burgers-complex Ginzburg-Landau （Burgers-CGL） equations, which are derived from the nonlinear evolution of the coupled long-scale oscillatory and monotonic instabilities of a uniformly propagating combustion wave governed by a sequential chem- ical reaction, having two flame fronts corresponding to two reaction zones with a finite separation distance between them. This paper firstly shows the existence of the global solutions to these coupled equations via subtle transforms, delicate a priori estimates and a so-called continuity method, then prove the existence of the global attractor and establish the estimates of the upper bounds of Hausdorff and fractal dimensions for the attractor.
文摘复Ginzburg-Landau (CGL)方程作为非平衡系统动力学的普适模型, 在量子流体动力学、 超导 理论及Bose-Einstein疑聚体等物理系统中具有重要应用, 适定性与渐近极限是其数学理论研究中 的重要方向。 本文针对具有混合耗散算子的CGL方程展开系统性研究。 通过混合耗散算子的正则 性分析与特定参数比率约束条件的构造, 确立L2解的唯一性, 井借助与耗散参数相关的截断函数及 能量估计方法, 揭示了耗散系数趋于0时, 从CGL方程到高阶非线性Schro¨dinger (NLS)方程的无 粘极限及其收敛速率。The complex Ginzburg-Landau (CGL) equation, as a universal model for non-equilibrium system dynamics, has important applications in physical systems such as quantum fluid dynamics, superconductivity theory, and Bose-Einstein condensates. Well-posedness and asymptotic limit are important directions in the study of mathematical theory.This article conducts a systematic study on the CGL equation with mixed dissipa- tive operators. By analyzing the regularity of the mixed dissipation operators and constructing specific parameter ratio constraints, the uniqueness of the L2 solution is established. With the help of truncation function and energy estimates related to dissipation parameters, the inviscid limit and convergence rate from CGL equation to high-order nonlinear Schro¨dinger (NLS) equation are obtained when the dissipation coefficients approaches to 0.
文摘In this paper, we are concerned with the existence and uniqueness of global solutions of the modified KS-CGL equations for flames governed by a sequential reaction, where the term ｜P｜2σP is replaced with the generalized form ｜P｜2P, see [18]. The main novelty compared with [18] in this paper is to control the norms of the first order of the solutions and extend the global well-posedness to three dimensional space.
