14 citations · 28 across the 12 of their papers we have counts for
13 papers
The Navier-Stokes equations with transport noise in critical space
Mustafa Sencer Aydın, Fanhui Xu
We study the Navier-Stokes equations with transport noise in critical function spaces. Assuming the initial data belongs to almost surely, we establish the existence and…
The stochastic Navier-Stokes equations with general data
Mustafa Sencer Aydın, Igor Kukavica, Fanhui Xu
We consider the stochastic Navier-Stokes equations with multiplicative noise with critical initial data. Assuming that the initial data belongs to the critical space …
Almost global existence for the stochastic Navier-Stokes equations with small data
Mustafa Sencer Aydın, Igor Kukavica, Fanhui Xu
We address the global existence of solutions to the stochastic Navier-Stokes equations with multiplicative noise and with initial data in . We prove that t…
Global existence of the stochastic Navier-Stokes equations in with small data
Igor Kukavica, Fanhui Xu
We address the global-in-time existence and pathwise uniqueness of solutions for the stochastic incompressible Navier-Stokes equations with a multiplicative noise on the three-dime…
No blow-up by nonlinear Itô noise for the Euler equations
Marco Bagnara, Mario Maurelli, Fanhui Xu
By employing a suitable multiplicative Itô noise with radial structure and with more than linear growth, we show the existence of a unique, global-in-time, strong solution for the…
Local existence of the stochastic Navier-Stokes equations in the whole space
Igor Kukavica, Fei Wang, Fanhui Xu
We address the local well-posedness for the stochastic Navier-Stokes system with multiplicative cylindrical noise in the whole space. More specifically, we prove that there exists…
Local existence of strong solutions to the stochastic Navier-Stokes equations with data
Igor Kukavica, Fanhui Xu
For the stochastic Navier-Stokes equations with a multiplicative white noise on , we prove that there exists a unique strong solution locally in time when the init…
Existence and uniqueness of solutions of SDEs with discontinuous drift and finite activity jumps
Paweł Przybyłowicz, Michaela Szölgyenyi, Fanhui Xu
In this letter we prove existence and uniqueness of strong solutions to multi-dimensional SDEs with discontinuous drift and finite activity jumps.
On some cadlaguity moment estimates of stochastic jump processes
R. Mikulevicius, Fanhui Xu
Using the results of X. Fernique on the compactness of distributions of cadlag random functions, we derive some cadlaguity moment estimates for stochastic processes with jumps.
On the Cauchy problem for integro-differential equations with space-dependent operators in generalized Hölder classes
Fanhui Xu
Parabolic integro-differential Kolmogorov equations with different space-dependent operators are considered in Hölder-type spaces defined by a scalable Lévy measure. Probabilistic…
On the Cauchy problem for nondegenerate parabolic integro-differential equations in the scale of generalized Hölder spaces
R. Mikulevicius, Fanhui Xu
Parabolic integro-differential non degenerate Cauchy problem is considered in the scale of Hölder spaces of functions whose regularity is defined by a radially O-regularly varying…
On the Cauchy problem for parabolic integro-differential equations in generalized Hölder spaces
Remigijus Mikulevičius, Fanhui Xu
An integro-differential Kolmogorov equation is considered in Hölder-type spaces defined by a scalable Lévy measure. Some properties of those spaces and estimates of the solution ar…
On the rate of convergence of strong Euler approximation for SDEs driven by Levy processes
R. Mikulevicius, Fanhui Xu
SDE driven by an -stable process, with Lipshitz continuous coefficient and -Hölder drift is considered. The existence and uniqueness of a strong solution…