共查询到10条相似文献,搜索用时 117 毫秒
1.
Linghai Zhang 《Journal of Differential Equations》2008,245(11):3470-3502
Let u=u(x,t,u0) represent the global strong/weak solutions of the Cauchy problems for the general n-dimensional incompressible Navier-Stokes equations
2.
Norbert Ortner 《Bulletin des Sciences Mathématiques》2003,127(10):835-843
L. Hörmander's extension of Ásgeirsson's mean value theorem states that if u is a solution of the inhomogeneous ultrahyperbolic equation (Δx−Δy)u=f, , , then
3.
Alessandro Ferriero 《Journal of Differential Equations》2010,249(10):2548-2560
In this work we prove that, if L(t,u,ξ) is a continuous function in t and u, Borel measurable in ξ, with bounded non-convex pieces in ξ, then any absolutely continuous solution to the variational problem
4.
Xicheng Zhang 《Journal of Mathematical Analysis and Applications》2008,346(1):336-339
In terms of two partial derivatives of any two components of velocity fields, we give a new criterion for the regularity of solutions of the Navier-Stokes equation in R3. More precisely, let u=(u1,u2,u3) be a weak solution in (0,T)×R3. Then u becomes a classical solution if any two functions of ∂1u1, ∂2u2 and ∂3u3 belong to Lθ(0,T;Lr(R3)) provided with , . 相似文献
5.
For a bounded domain Ω in , N?2, satisfying a weak regularity condition, we study existence of positive and T-periodic weak solutions for the periodic parabolic problem Luλ=λg(x,t,uλ) in , uλ=0 on . We characterize the set of positive eigenvalues with positive eigenfunctions associated, under the assumptions that g is a Caratheodory function such that ξ→g(x,t,ξ)/ξ is nonincreasing in (0,∞) a.e. satisfying some integrability conditions in (x,t) and
6.
Yoshikazu Giga 《Journal of Mathematical Analysis and Applications》2006,316(2):538-555
A nonnegative blowing up solution of the semilinear heat equation ut=Δu+up with p>1 is considered when initial data u0 satisfies
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8.
Le Thi Phuong Ngoc Le Khanh Luan Tran Minh Thuyet Nguyen Thanh Long 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5799-5819
In this paper, we consider the following nonlinear wave equation (1) where , , μ, f, g are given functions. To problem (1), we associate a linear recursive scheme for which the existence of a local and unique weak solution is proved by applying the Faedo–Galerkin method and the weak compact method. In the case of , , μ(z)≥μ0>0, μ1(z)≥0, for all , and , , , a weak solution uε1,ε2(x,t) having an asymptotic expansion of order N+1 in two small parameters ε1, ε2 is established for the following equation associated to (1)2,3: (2) 相似文献
9.
Zhilei Liang 《Journal of Differential Equations》2009,246(1):391-134
In this paper we study the strict localization for the p-Laplacian equation with strongly nonlinear source term. Let u:=u(x,t) be a solution of the Cauchy problem
10.
Alberto Farina 《Journal of Differential Equations》2011,250(12):4367-4436
A famous theorem of Sergei Bernstein says that every entire solution u=u(x), x∈R2, of the minimal surface equation