共查询到20条相似文献,搜索用时 203 毫秒
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研究不可压Navier-Stokes方程初值在嵋(Rqσ) (q>n≥2或q=n≥3)上弱解的全局存在性,推广了C.P.Calderon的初值在Lqσ(Rn)(2≤q<n),n=3,4的结果.作为应用,对任意的k>0,给定初值f(x)=K(0,-x3/|x|2,x2/|x|2),Naver-Stokes方程都有一个全局弱解. 相似文献
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不可压流体的边界层问题 总被引:1,自引:0,他引:1
研究三维有界区域在边界上有流动的不可压流体的边界层问题,导出了Navier-Stokes方程区域内部的近似方程(Euler方程和线性化的Euler方程)和边界附近近似的方程(零阶边界层方程与一阶边界层方程),证明了这种近似的合理性. 相似文献
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给定初始涡度场ω_0属于L~(3/2)∩L~2,本文证明若三维不可压Navier-Stokes方程的Fujita-Kato解在有限时刻T~?处发生爆破,则对任意p∈[4,∞], q_1∈[1, 2],μ 0, q_2∈[2,(1/p+μ)~(-1)],κ∈[1,∞],以及任意单位向量e,(v(t)|e)_(R~3)的■范数等于无穷. 相似文献
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利用解析性估计和方程非线性项的特殊结构,本文证明了三维各向异Navier-Stokes方程对一类在垂直方向慢变的大初值的整体适定性. 相似文献
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§1.引言不可压Navier-Stokes(INS)方程在二维情况下可写为 ?u/?x+?v/?y=0, 相似文献
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《数学的实践与认识》2019,(23)
研究了三维不可压粘性Navier-Stokes方程的线性不稳定性.即当流体处在重力场时,若稳态密度有一定的连续性并随着高度的增加而增加时(即Rayleigh-Taylor密度),重力场中的Navier-Stokes流体是线性不稳定的.利用变分法解出线性方程的线性不稳定解. 相似文献
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In this paper,we establish the global well-posedness of the generalized rotating magnetohydrodynamics equations if the initial data are in X~(1-2α) defined by X~(1-2α)={u∈D'(R~3):∫_(R~3)|ξ|~(1-2α)|(ξ)|dξ+∞}.In addition,we also give Gevrey class regularity of the solution. 相似文献
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Cauchy Problem for Semilinear Wave Equations in Four Space Dimensions with Small Initial Data 下载免费PDF全文
Yi Zhou 《偏微分方程(英文版)》1995,8(2):135-144
In this paper, we consider the Cauchy problem ◻u(t,x) = |u(t,x)|^p, (t,x) ∈ R^+ × R^4 t = 0 : u = φ(x), u_t = ψ(x), x ∈ R^4 where ◻ = ∂²_t - Σ^4_{i=1}∂²_x_i, is the wave operator, φ, ψ ∈ C^∞_0 (R^4). We prove that for p > 2 the problem has a global solution provided tile initial data is sufficiently small. 相似文献
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非线性Klein-Gordon方程柯西问题解的整体存在性与Blow-up 总被引:2,自引:0,他引:2
研究非线性Klein-Gordon方程的柯西问题u_(tt)-Δu+u=u|u|~(p-1),x∈R~n,t>0;u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈R~n.通过引进一族位势井,得到了解的整体存在性与不存在的门槛结果. 相似文献
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Weiliang Xiao & Xuhuan Zhou 《数学研究》2020,53(3):316-328
We study a kind of generalized porous medium equation with fractional Laplacian and abstract pressure term. For a large class of equations corresponding to the form: $u_t+\nu \Lambda^{\beta}u=\nabla\cdot(u\nabla Pu)$, we get their local well-posedness in Fourier-Besov spaces for large initial data. If the initial data is small, then the solution becomes global. Furthermore, we prove a blowup criterion for the solutions. 相似文献
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In this paper,we consider the global well-posedness of smooth solutions for the Cauchy problem of a sixth order convective Cahn-Hilliard equation with small initial data.We first construct a local smooth solution,then by combining some a priori estimates,continuity argument,the local smooth solution is extended step by step to all t>0 provided that the L1 norm of initial data is suitably small and the smooth nonlinear functions f(u)and g(u)satisfy certain local growth conditions at some fixed point■. 相似文献
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《数学学报》2014,(3)
<正>The Defocusing Energy-supercritical Hartree Equation Ji Qiang ZHENGAbstract In this paper,we study the global well-posedness and scattering problem for the energy-supercritical Hartree equation iu_t+△u-(|x|~(-γ)*|u|~2)u=0 withγ4 in dimension dγ.We prove that if the solution u is apriorily bounded in the critical Sobolev space,that is,u∈L_t~∞(I;H_x~sc(R~d))with s_c:=γ/2-11,then u is global and scatters.The impetus to 相似文献
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本文讨论了如下一类非线性薛定谔方程:-△u+V(x)u=f(u),x∈R^N,在H^1(R^N)中无穷多解的存在性,其中N≥3,V(x)是RN上的实值连续函数并且满足对(A)x∈R^N,V(z)≥V0>0. 相似文献
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本文讨论了出现在双色谱中的非线性双曲型守恒律组的如下Cauchy问题{ut+(u/1+u+v)x=0,vt+(v/1+u+v)x=0,初值为u(x,0)=u0(x),v(x,0)=v0(x)的整体光滑解的存在性和唯一性.分析过程基于对角化方法和特征线法. 相似文献
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Well-posedness,global existence,and blowup phenomena for a periodic quasi-linear hyperbolic equation
We establish the local well-posedness of a recently derived model for small-amplitude, shallow water waves. For a large class of initial data we prove global existence of the corresponding solution. Criteria guaranteeing the development of singularities in finite time for strong solutions with smooth initial data are obtained, and an existence and uniqueness result for a class of global weak solutions is also given. © 1998 John Wiley & Sons, Inc. 相似文献