5 papers
Remarks on the convex integration technique applied to singular stochastic partial differential equations
Hongjie Dong, Kazuo Yamazaki
Singular stochastic partial differential equations informally refer to the partial differential equations with rough random force that leads to the products in the nonlinear terms…
Remarks on the three-dimensional Navier-Stokes equations with Lions' exponent forced by space-time white noise
Kazuo Yamazaki
We study the three-dimensional Navier-Stokes equations forced by space-time white noise and diffused via the fractional Laplacian with Lions' exponent so that it is precisely the e…
On Ricci Solitons with Isoparametric Potential Functions
Hung Tran, Kazuo Yamazaki
This paper studies a complete gradient Ricci soliton with an isoparametric potential function. Our first theorem asserts that, for the steady case, there is a critical level set of…
Global unique solution to the perturbation of the Burgers' equation forced by derivatives of space-time white noise
Kazuo Yamazaki
We consider the one-dimensional Burgers' equation forced by fractional derivative of order applied on space-time white noise. Relying on the approaches of Anderson Ha…
Stochastic magnetohydrodynamics system: cross and magnetic helicity in ideal case; non-uniqueness up to Lions' exponents from prescribed initial data
Kazuo Yamazaki
We consider the three-dimensional magnetohydrodynamics system forced by random noise. First, for smooth solutions in the ideal case, the cross helicity remains invariant while the…