25 citations · 156 across the 24 of their papers we have counts for
25 papers
Remarks on the two-dimensional magnetohydrodynamics system forced by space-time white noise
Kazuo Yamazaki
We study the two-dimensional magnetohydrodynamics system forced by space-time white noise. Due to a lack of an explicit invariant measure, the approach of Da Prato and Debussche (2…
Another remark on the global regularity issue of the Hall-magnetohydrodynamics system
Mohammad Mahabubur Rahman, Kazuo Yamazaki
We discover cancellations upon -estimate of the Hall term for . As its consequence, first, we derive a regularity criterion for the 3-dimensio…
Non-uniqueness in law of the two-dimensional surface quasi-geostrophic equations forced by random noise
Kazuo Yamazaki
Via probabilistic convex integration, we prove non-uniqueness in law of the two-dimensional surface quasi-geostrophic equations forced by random noise of additive type. In its proo…
Remarks on the global regularity issue of the two and a half dimensional Hall-magnetohydrodynamics system
Mohammad Mahabubur Rahman, Kazuo Yamazaki
Whether or not the solution to the -dimensional Hall-magnetohydrodynamics system starting from smooth initial data preserves its regularity for all time remains a cha…
Non-uniqueness in law of transport-diffusion equation forced by random noise
Ujjwal Koley, Kazuo Yamazaki
We consider a transport-diffusion equation forced by random noise of three types: additive, linear multiplicative in It's interpretation, and transport in Straton…
Regularity criteria for the Kuramoto-Sivashinsky equation in dimensions two and three
Adam Larios, Mohammad Mahabubur Rahman, Kazuo Yamazaki
We propose and prove several regularity criteria for the 2D and 3D Kuramoto-Sivashinsky equation, in both its scalar and vector forms. In particular, we examine integrability crite…
Non-uniqueness in law of three-dimensional magnetohydrodynamics system forced by random noise
Kazuo Yamazaki
We prove non-uniqueness in law of the three-dimensional magnetohydrodynamics system that is forced by random noise of an additive and a linear multiplicative type and has viscous a…
Non-uniqueness in law of three-dimensional Navier-Stokes equations diffused via a fractional Laplacian with power less than one half
Kazuo Yamazaki
Non-uniqueness of three-dimensional Euler equations and Navier-Stokes equations forced by random noise, path-wise and more recently even in law, have been proven by various authors…
Non-uniqueness in law for Boussinesq system forced by random noise
Kazuo Yamazaki
Non-uniqueness in law for three-dimensional Navier-Stokes equations forced by random noise was established recently in Hofmanov et al. (2019, arXiv:1912.11841 […
Non-uniqueness in law for two-dimensional Navier-Stokes equations with diffusion weaker than a full Laplacian
Kazuo Yamazaki
We study the two-dimensional Navier-Stokes equations forced by random noise with a diffusive term generalized via a fractional Laplacian that has a positive exponent strictly less…
Remarks on the non-uniqueness in law of the Navier-Stokes equations up to the J.-L. Lions' exponent
Kazuo Yamazaki
Lions (1959, Bull. Soc. Math. France, \textbf{87}, 245--273) introduced the Navier-Stokes equations with a viscous diffusion in the form of a fractional Laplacian; subsequently, he…
Three-dimensional magnetohydrodynamics system forced by space-time white noise
Kazuo Yamazaki
We consider the three-dimensional magnetohydrodynamics system forced by noise that is white in both time and space. Its complexity due to four non-linear terms makes its analysis v…
On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation
Adam Larios, Kazuo Yamazaki
The Kuramoto-Sivashinsky equations (KSE) arise in many diverse scientific areas, and are of much mathematical interest due in part to their chaotic behavior, and their similarity t…
Ergodicity of a Galerkin approximation of three-dimensional magnetohydrodynamics system forced by a degenerate noise
Kazuo Yamazaki
Magnetohydrodynamics system consists of a coupling of the Navier-Stokes and Maxwell's equations and is most useful in studying the motion of electrically conducting fluids. We prov…
Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model
Kazuo Yamazaki, Xueying Wang
We study the global stability issue of the reaction-convection-diffusion cholera epidemic PDE model and show that the basic reproduction number serves as a threshold parameter that…
Regularity criteria of the three-dimensional MHD system involving one velocity and one vorticity component
Kazuo Yamazaki
We obtain a regularity criteria of the solution to the three-dimensional magnetohydrodynamics system to remain smooth for all time involving only one velocity and one vorticity com…
On the three-dimensional magnetohydrodynamics system in scaling-invariant spaces
Kazuo Yamazaki
We study the criterion for the velocity and magnetic vector fields that solve the three-dimensional magnetohydrodynamics system, given any initial data sufficiently smooth, to expe…
Regularity criterion of the 4D Navier-Stokes equations involving two velocity field components
Kazuo Yamazaki
We study the Serrin-type regularity criteria for the solutions to the four-dimensional Navier-Stokes equations and magnetohydrodynamics system. We show that the sufficient conditio…
A remark on the two-dimensional magneto-hydrodynamics-alpha system
Kazuo Yamazaki
We study the two-dimensional generalized magnetohydrodynamics- system with fractional Laplacians in the dissipative and diffusive terms. We show that the solution pair of veloci…
Remarks on the global regularity of two-dimensional magnetohydrodynamics system with zero dissipation
Kazuo Yamazaki
We study the two-dimensional generalized magnetohydrodynamics system with generalized dissipation and diffusion in terms of fractional Laplacians. It is known that the classical ma…
Remarks on the regularity criteria of generalized MHD and Navier-Stokes systems
Kazuo Yamazaki
We study the regularity criteria of the three dimensional generalized MHD and Navier-Stokes systems. In particular, we show that the regularity criteria of the generalized MHD syst…
On the global regularity of two-dimensional generalized magnetohydrodynamics system
Kazuo Yamazaki
We study the two-dimensional generalized magnetohydrodynamics system with dissipation and diffusion in terms of fractional Laplacians. In particular, we show that in case the diffu…
Global regularity of logarithmically supercritical MHD system with zero diffusivity
Kazuo Yamazaki
We prove the global regularity of the solution pair to the N-dimensional logarithmically supercritical magnetohydrodynamics system with zero diffusivity. This is the endpoint case…
A Remark on the Global Well-posedness of a Modified Critical Quasi-geostrophic Equation
Kazuo Yamazaki
The -generalized quasi-geostrophic equation is studied in the range of . When such that $1 \leq α+ β<…