We show that a suitable weak solution to the incompressible Navier–Stokes equations on R3×(?1,1) is regular R3×(?1,0] if ?3u belongs M2p/(2p?3),?((?1,0);Lp(R3)) for any ?>1 and p?(3/2,?), which logarithmic-type variation of Morrey space in time. For each this is, up logarithm, critical with respect scaling equations, contains all spaces Lq((?1,0);Lp(R3)) are subcritical, 2/q+3/p<2.

Our main purpose of this article is to study the convergence and other related properties q-Bernstein-Kantorovich operators including shifted knots real positive numbers. We design Bernstein-Kantorovich generated by basic q-calculus. More precisely, we our new in space continuous functions Lebesgue space. obtain degree with help modulus continuity integral continuity. Furthermore, establish qua...

We give necessary and sufficient conditions for the boundedness of generalized fractional integral maximal operators on Orlicz–Morrey weak spaces. To do this, we prove weak–weak type modular inequality Hardy–Littlewood operator with respect to Young function. spaces contain L p $L^p$ ( 1 ≤ ∞ $1\le p\le \infty$ ), Orlicz spaces, Morrey as special cases. Hence, get these function corollaries.

This paper concerns a family of weak parallelogram laws for Banach spaces. It is shown that the familiar Lebesgue spaces satisfy a range of these inequalities. Connections are made to basic geometric ideas, such as smoothness, convexity, and Pythagorean-type theorems. The results are applied to the linear prediction of random processes spanning a Banach space. In particular, theweak parallelogr...

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Blow-up criteria of smooth solutions for the 3D micropolar fluid equations are investigated. Logarithmically improved blow-up criteria are established in the Morrey-Campanto space.

We establish the global well-posedness of the Landau-Lifshitz-Gilbert equation in Rn for any initial data m0 ∈ H1 ∗(R, S2) whose gradient belongs to the Morrey space M2,2(Rn) with small norm ‖∇m0‖M2,2(Rn). The method is based on priori estimates of a dissipative Schrödinger equation of GinzburgLandau types obtained from the Landau-Lifshitz-Gilbert equation by the moving frame technique.

For an arbitrary in nite-dimensional Banach space X, we construct examples of strongly-measurable X-valued Pettis integrable functions whose indefinite Pettis integrals are nowhere weakly di erentiable; thus, for these functions the Lebesgue Di erentiation Theorem fails rather spectacularly. We also relate the degree of nondi erentiability of the inde nite Pettis integral to the cotype of X, fr...