Zobrazeno 1 - 10
of 381
pro vyhledávání: '"Kukavica, Igor"'
Autor:
Kukavica, Igor, Xu, Fanhui
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-dimensional torus. Under natural smallness conditions on the noise, we pro
Externí odkaz:
http://arxiv.org/abs/2410.02919
Autor:
Kukavica, Igor, Ożański, Wojciech S.
We consider the three-dimensional ideal MHD system on a domain $\Omega' \subset \mathbb{R}^3$ with a part $\Gamma$ of the boundary~$\partial \Omega$, where we prescribe both $u\cdot n$ and $b\cdot n$, while $u\cdot n = b\cdot n =0$ on $\partial \Omeg
Externí odkaz:
http://arxiv.org/abs/2410.02588
We consider the size of the nodal set of the solution of the second order parabolic-type equation with Gevrey regular coefficients. We provide an upper bound as a function of time. The dependence agrees with a sharp upper bound when the coefficients
Externí odkaz:
http://arxiv.org/abs/2409.09879
Autor:
Aydın, Mustafa Sencer, Kukavica, Igor
We consider the three-dimensional incompressible Euler equations in Sobolev conormal spaces and establish local-in-time existence and uniqueness in the half-space or channel. The initial data is Lipschitz having four square-integrable conormal deriva
Externí odkaz:
http://arxiv.org/abs/2407.18149
We give a novel vorticity formulation for the 3D Navier-Stokes equations with Dirichlet boundary conditions. Via a resolvent argument, we obtain Green's function and establish an upper bound, which is the 3D analog of [24]. Moreover, we prove similar
Externí odkaz:
http://arxiv.org/abs/2407.10751
Autor:
Aydın, Mustafa Sencer, Kukavica, Igor
We consider the vanishing viscosity problem for solutions of the Navier-Stokes equations with Navier boundary conditions in the half-space. We lower the currently known conormal regularity needed to establish that the inviscid limit holds. Our requir
Externí odkaz:
http://arxiv.org/abs/2404.17111
We consider the Cauchy problem for an inviscid irrotational fluid on a domain with a free boundary governed by a fourth order linear elasticity equation. We first derive the Craig-Sulem-Zakharov formulation of the problem and then establish the exist
Externí odkaz:
http://arxiv.org/abs/2404.09820
On the local existence of solutions to the fluid-structure interaction problem with a free interface
We address a system of equations modeling an incompressible fluid interacting with an elastic body. We prove the local existence when the initial velocity belongs to the space $H^{1.5+\epsilon}$ and the initial structure velocity is in $H^{1+\epsilon
Externí odkaz:
http://arxiv.org/abs/2312.16395
We address a free boundary model for the compressible Euler equations where the free boundary, which is elastic, evolves according to a weakly damped fourth order hyperbolic equation forced by the fluid pressure. This system captures the interaction
Externí odkaz:
http://arxiv.org/abs/2311.08731
We consider the incompressible Euler equation on an analytic domain $\Omega $ with nonhomogeneous boundary condition $u\cdot \mathsf{n} = \overline{u} \cdot \mathsf{n}$ on $\partial \Omega$, where $\overline{u}$ is a given divergence-free analytic ve
Externí odkaz:
http://arxiv.org/abs/2310.20439