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1.
带密度的不可压Euler方程在临界Besov空间中的适定性   总被引:1,自引:0,他引:1       下载免费PDF全文
本文证明了带密度的不可压Euler方程在临界Besov空间中的局部适定性,并且只用涡度场给出了强解的一个爆破准则.另外,本文关于带密度的不可压磁流体方程得到了类似结果.  相似文献   

2.
研究了一个广义两分量Camassa-Holm方程的柯西问题,该模型可从经过线性切流的浅水波的理论机制中得出.文中讨论了该模型的爆破现象,建立了爆破发生时柯西问题的初始值满足的充分条件.同时研究了强解的持久和唯一连续性.  相似文献   

3.
一类弱耗散双组份Hunter-Saxton系统的爆破与爆破率   总被引:1,自引:0,他引:1  
研究了一类周期弱耗散双组份Hunnter-Saxton系统的爆破现象.首先,给出了此类Hunnter-Saxton系统解的局部适定性及其精确的爆破机制;其次,证明了在一定的初始值下Hunnter-Saxton系统强解的几个爆破结果;最后,给出了HunnterSaxton系统强解的爆破率.  相似文献   

4.
该文讨论了在真空远场的密度条件下,二维不可压零磁耗散磁流体力学方程组柯西问题的局部适定性.在初始密度和磁场具有一定的衰减性时,证明了磁流体方程具有唯一的局部强解.当初值满足兼容性条件和适当的正则性条件时,该强解就是经典解.除此之外,文中还给出了一个仅与磁场有关的爆破准则.  相似文献   

5.
主要研究了一类带有非牛顿位势的可压缩Navier-Stokes方程:其中粘性系数μ依赖于密度ρ,Φ是非牛顿位势.证明了上述问题的强解的存在性.在相容性条件下,得到了强解的唯一性.  相似文献   

6.
考虑一般的两个分量的Dullin-Gottwald-Holm(GDGH2)系统解的爆破和无限传播速度.首先,给出了一个保证强解发生爆破的新的充分条件.然后,证明了对GDGH2的非平凡古典解而言,初始值u_0(x)和ρ_0(x)有紧支集不能保证相应的解有紧支集.  相似文献   

7.
考查了周期边界条件下的磁流体方程,证明了它的解关于时间是解析的,由此得到了磁流体方程的解的向后惟一性.对于周期解,证明了当周期小于某个常数时,周期的弱解是强解,进一步地这样的强解是定常解.  相似文献   

8.
引入了主算子为n次积分C半群生成元的线性非齐次抽象柯西问题强解的概念,讨论了相应抽象柯西问题存在强解的一些充分必要条件及强解的表示式.并给出了一个例子验证结果.  相似文献   

9.
对来自金融数学领域的方程xxu+uyu-tu=c(x,y,t,u),(x,y,t)∈QT=R2×[0,T)的Cauchy问题,给出了一种新的熵解的定义,得到了其适定性结果.可以证明所得到的解还是强解,即方程中所出现的各阶偏导数几乎处处连续.最后讨论了解的爆破性质以及与解的间断点相关的几何性质.  相似文献   

10.
用Galerkin方法研究了一类非线性波动方程的初边值问题,证明其在一定条件下强解的存在性.  相似文献   

11.
In this paper, a discretization of a semilinear wave equation whose nonlinear term is a power function is investigated. It is shown that, when a condition on the initial value problem, similar to that governing the existence of blow-up solutions for the original continuous equation is met, the newly introduced difference equation has blow-up solutions with characteristics corresponding to those of the blow-up solutions for the original equation.  相似文献   

12.
Qing Han 《偏微分方程通讯》2013,38(12):2199-2237
The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up behavior are given, and it is shown that blow-up solutions are not unique.  相似文献   

13.
The main purpose here is the study of dispersive blow-up for solutions of the Zakharov-Kuznetsov equation. Dispersive blow-up refers to point singularities due to the focusing of short or long waves. We will construct initial data such that solutions of the linear problem present this kind of singularities. Then we show that the corresponding solutions of the nonlinear problem present dispersive blow-up inherited from the linear component part of the equation. Similar results are obtained for the generalized Zakharov-Kuznetsov equation.  相似文献   

14.
In this paper we study several qualitative properties of the Degasperis-Procesi equation. We first established the precise blow-up rate and then determine the blow-up set of blow-up strong solutions to this equation for a large class of initial data. We finally prove the existence and uniqueness of global weak solutions to the equation provided the initial data satisfies appropriate conditions.  相似文献   

15.
Growth estimate of positive solution for a quasilinear parabolic equation subject to Robin boundary condition is presented by the maximum principles. The growth estimate is then used to study blow-up of the solution of the problem. The bounds of ‘blow-up time’ and blow-up rate are obtained.  相似文献   

16.
Using a variational approach we prove an optimal nonlinear convolution inequality. This result is then applied to give criteria for finite-time blow-up of solutions to a nonlinear model equation in elasticity, improving considerably upon recent blow-up results.  相似文献   

17.
We mainly study the Cauchy problem of the periodic generalized Degasperis-Procesi equation. First, we establish the local well-posedness for the equation. Second, we give the precise blow-up scenario, a conservation law and prove that the equation has smooth solutions which blow up in finite time. Finally, we investigate the blow-up rate for the blow-up solutions.  相似文献   

18.
In this paper, we consider a generalized Camassa–Holm equation with the flow generated by the vector field and its gradient. We first establish the local well-posedness of equation in the sense of Hadamard in both critical Besov spaces and supercritical Besov spaces. Then we gain a blow-up criterion. Under a sign condition we reach the sign-preserved property and a precise blow-up criterion. Applying this precise criterion we finally present two blow-up results and the precise blow-up rate for strong solutions to equation.  相似文献   

19.
This paper studies the blow-up solution and its blow-up rate near the traveling waves of the second-order Camassa–Holm equation. The sufficient condition for the existence of blow-up solution is obtained by a rather ingenious method. Applying the extended pseudo-conformal transformation, an equivalent proposition of the solution breaking in finite time near the traveling waves is constructed. The relation is established between the blow-up time and rate of the solution and the residual’s.  相似文献   

20.
In this article, we consider a newly modified two-component Camassa–Holm equation. First, we establish the local well-posedness result, then we present a precise blow-up scenario. Afterwards, we derive a new conservation law, by which and the precise blow-up scenario we prove three blow-up results and a blow-up rate estimate result.  相似文献   

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