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1.
In this paper, the authors study the equation ut=div(|Du|p−2Du)+|u|q−1uλl|Du| in RN with p>2. We first prove that for 1?l?p−1, the solution exists at least for a short time; then for , the existence and nonexistence of global (in time) solutions are studied in various situations.  相似文献
2.
The aim of this paper is to discuss the Cauchy problem of the quasilinear hyperbolic equation of the form
ut+x(um)=up  相似文献
3.
In this paper we consider the Yudovich type solution of the 2D inviscid Boussinesq system with critical and supercritical dissipation. For the critical case, we show that the system admits a global and unique Yudovich type solution; for the supercritical case, we prove the local and unique existence of Yudovich type solution, and the global result under a smallness condition of θ0θ0. We also give a refined blowup criterion in the supercritical case.  相似文献
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5.
This paper deals with a class of coupled systems of parabolic equations subject to large initial data. By constructing and solving a new ODE system, we obtain the accurate life span of solutions (blow-up time) of the expression determined by the initial value.  相似文献
6.
The goal of this work is to study the Boussinesq equations for an incompressible fluid in R2, with diffusion modeled by fractional Laplacian. The existence, the uniqueness and the regularity of solution has been proved.  相似文献
7.
The aims of this paper are to discuss global existence and uniqueness of solution for a class of non-Newtonian fluids with vacuum in one-dimensional bounded interval. The important point in this paper is that we allow the initial vacuum. In particular, these results are used to prove similar results for more general non-Newtonian fluids, and applied to numerical computation. This work is partially supported by the 985 program of Jilin University, China Postdoctoral Sciences Foundation, and NSF Grant ([10571072]; [10601009]).  相似文献
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9.
The aim of this paper is two-fold. Given a recollement (T′, T, T″, i*, i*, i!, j!, j*, j*), where T′, T, T″ are triangulated categories with small coproducts and T is compactly generated. First, the authors show that the BBD-induction of compactly generated t-structures is compactly generated when i* preserves compact objects. As a con-sequence, given a ladder (T′, T, T″, T, T′) of height 2, then the certain BBD-induction of compactly generated t-structures is compactly generated. The authors apply them to the recollements induced by homological ring epimorphisms. This is the first part of their work. Given a recollement (D(B-Mod),D(A-Mod),D(C-Mod), i*, i*, i!, j!, j*, j*) induced by a homological ring epimorphism, the last aim of this work is to show that if A is Gorenstein, A B has finite projective dimension and j! restricts to D b (C-mod), then this recollement induces an unbounded ladder (B-Gproj,A-Gproj, C-Gproj) of stable categories of finitely generated Gorenstein-projective modules. Some examples are described.  相似文献
10.
The paper is devoted to the existence and uniqueness of local solutions for the density‐dependent non‐Newtonian compressible fluids with vacuum in one‐dimensional bounded intervals. The important points in this paper are that the initial density may vanish in an open subset and the viscosity coefficient is nonlinearly dependent of density and shear rate.  相似文献
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