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In this paper, we mainly study the local energy equation of the weak solutions of the compressible isentropic MHD equation defined on . We prove that the regularity of the solution is sufficient to guarantee the balance of the total energy in the space. We adopt a variant of the method of Feireisl et al. 相似文献
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In this paper, we study the existence of ground state solutions for the modified fractional Schrödinger equations where , , , and are positive parameters, , denotes the fractional Laplacian of order . For the case and the case , the existence results of ground state solutions are given, respectively. 相似文献
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Dongping Li Fangqi Chen Yonghong Wu Yukun An 《Mathematical Methods in the Applied Sciences》2022,45(1):515-531
In this paper, we focus on a class of generalized (p, q)-Laplacian-type impulsive fractional differential equation for 1 < p≤q < ∞, with a nonlinearity f containing fractional derivatives and simultaneously and being imposed on mild assumptions contrasting with previous works. The underlying idea is based on the Mountain pass theorem and the iterative technique to obtain the existence of nontrivial solutions for our equation. Our work extends and supplements some existing results. 相似文献
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This article examines the existence and uniqueness of weak solutions to the d‐dimensional micropolar equations (d=2 or d=3) with general fractional dissipation (?Δ)αu and (?Δ)βw. The micropolar equations with standard Laplacian dissipation model fluids with microstructure. The generalization to include fractional dissipation allows simultaneous study of a family of equations and is relevant in some physical circumstances. We establish that, when and , any initial data (u0,w0) in the critical Besov space and yields a unique weak solution. For α ≥ 1 and β=0, any initial data and also leads to a unique weak solution as well. The regularity indices in these Besov spaces appear to be optimal and can not be lowered in order to achieve the uniqueness. Especially, the 2D micropolar equations with the standard Laplacian dissipation, namely, α=β=1, have a unique weak solution for . The proof involves the construction of successive approximation sequences and extensive a priori estimates in Besov space settings. 相似文献
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Stevo Stevi 《Mathematical Methods in the Applied Sciences》2022,45(1):546-556
We investigate the following multilinear integral operator where and is a continuous kernel function satisfying the condition for some functions , which are continuous, increasing, , and a function , from a product of weighted-type spaces to weighted-type spaces of real functions. We calculate the norm of the operator, extending and complementing some results in the literature. We also give an explanation for a relation between integrals of an Lp integrable function and its radialization on . 相似文献
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In this paper, we study the following Schrödinger-Poisson equations: where , is a parameter and and satisfy the critical frequency conditions. By using variational methods and penalization arguments, we show the existence of multibump solutions for the above system. Furthermore, the heights of these bumps are different order. 相似文献
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We give necessary and sufficient conditions for the boundedness of generalized fractional integral and maximal operators on Orlicz–Morrey and weak Orlicz–Morrey spaces. To do this, we prove the weak–weak type modular inequality of the Hardy–Littlewood maximal operator with respect to the Young function. Orlicz–Morrey spaces contain spaces (), Orlicz spaces, and generalized Morrey spaces as special cases. Hence, we get necessary and sufficient conditions on these function spaces as corollaries. 相似文献
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In this article, we study the blow‐up of the damped wave equation in the scale‐invariant case and in the presence of two nonlinearities. More precisely, we consider the following equation: with small initial data. For and μ ∈ (0, μ?) , where μ? > 0 is depending on the nonlinearties' powers and the space dimension (μ? satisfies ), we prove that the wave equation, in this case, behaves like the one without dissipation (μ = 0 ). Our result completes the previous studies in the case where the dissipation is given by , where, contrary to what we obtain in the present work, the effect of the damping is not significant in the dynamics. Interestingly, in our case, the influence of the damping term is important. 相似文献
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Jia‐Feng Liao 《Mathematical Methods in the Applied Sciences》2021,44(1):407-418
In this article, we devote ourselves to investigate the following singular Kirchhoff‐type equation: where is a bounded domain with smooth boundary ?Ω,0∈Ω,a≥0,b,λ>0,0<γ,s<1, and By using the variational and perturbation methods, we obtain the existence of two positive solutions, which generalizes and improves the recent results in the literature. 相似文献
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Brahim Alouini 《Mathematical Methods in the Applied Sciences》2021,44(1):91-103
In this article, we present, throughout two basic models of damped nonlinear Schrödinger (NLS)–type equations, a new idea to bound from above the fractal dimension of the global attractors for NLS‐type equations. This could answer the following open issue: consider, for instance, the classical one‐dimensional cubic nonlinear Schrödinger equation “How can we bound the fractal dimension of the associate global attractor without the need to assume that the external forcing term f has some decay at infinity (that is belonging to some weighted Lebesgue space)?” 相似文献
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Yaning Wang 《Mathematische Nachrichten》2021,294(1):195-206
Let M be a Hopf hypersurface in a nonflat complex space form , , of complex dimension two. In this paper, we prove that M has η‐recurrent Ricci operator if and only if it is locally congruent to a homogeneous real hypersurface of type (A) or (B) or a non‐homogeneous real hypersurface with vanishing Hopf principal curvature. This is an extension of main results in [17, 21] for real hypersurfaces of dimension three. By means of this result, we give some new characterizations of Hopf hypersurfaces of type (A) and (B) which generalize those in [14, 18, 26]. 相似文献
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In this paper, we concern with the following fractional p‐Laplacian equation with critical Sobolev exponent where ε > 0 is a small parameter, λ > 0 , N is a positive integer, and N > ps with s ∈ (0, 1) fixed, . Since the nonlinearity does not satisfy the following Ambrosetti‐Rabinowitz condition: with μ > p , it is difficult to obtain the boundedness of Palais‐Smale sequence, which is important to prove the existence of positive solutions. In order to overcome the above difficulty, we introduce a penalization method of fractional p‐Laplacian type. 相似文献
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We provide a characterization for the existence and uniqueness of solutions in the space of vector‐valued sequences for the multiterm fractional delayed model in the form where X is a Banach space, A is a closed linear operator with domain D(A) defined on X, and ΔΓ denotes the Grünwald–Letkinov fractional derivative of order Γ > 0. We also give some conditions to ensure the existence of solutions when adding nonlinearities. Finally, we illustrate our results with an example given by a general abstract nonlinear model that includes the fractional Fisher equation with delay. 相似文献
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In this paper, we prove the large‐time behavior, as time tends to infinity, of solutions in and for a system modeling the nematic liquid crystal flow, which consists of a subsystem of the compressible Navier‐Stokes equations coupling with a subsystem including a heat flow equation for harmonic maps. 相似文献
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Jiabin Zuo Tianqing An Alessio Fiscella 《Mathematical Methods in the Applied Sciences》2021,44(1):1071-1085
The paper deals with the following Kirchhoff‐type problem where M models a Kirchhoff coefficient, is a variable s(·) ‐order p(·) ‐fractional Laplace operator, with and . Here, is a bounded smooth domain with N > p(x, y)s(x, y) for any , μ is a positive parameter, g is a continuous and subcritical function, while variable exponent r(x) could be close to the critical exponent , given with and for . We prove the existence and asymptotic behavior of at least one non‐trivial solution. For this, we exploit a suitable tricky step analysis of the critical mountain pass level, combined with a Brézis and Lieb‐type lemma for fractional Sobolev spaces with variable order and variable exponent. 相似文献
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Tran van Trung 《组合设计杂志》2020,28(3):261-270
Hyperovals in projective planes turn out to have a link with t‐designs. Motivated by an unpublished work of Lonz and Vanstone, we present a construction for t‐designs and s‐resolvable t‐designs from hyperovals in projective planes of order . We prove that the construction works for . In particular, for the construction yields a family of 5‐ designs. For numerous infinite families of 4‐designs on points with block size can be constructed for any . The construction assumes the existence of a 4‐ design, called the indexing design, including the complete 4‐ design. Moreover, we prove that if the indexing design is s‐resolvable, then so is the constructed design. As a result, many of the constructed designs are s‐resolvable for . We include a short discussion on the simplicity or non‐simplicity of the designs from hyperovals. 相似文献