71 citations · 278 across the 57 of their papers we have counts for
63 papers
Exponential Decay of Solutions to a Fluid-Plate Model with Small Initial Data
Mario Bukal, Igor Kukavica, Linfeng Li +1
We consider a three-dimensional fluid-structure interaction problem coupling the incompressible Navier-Stokes equations in a time-dependent domain with a square-root damped plate e…
Analyticity up to the boundary for the divergence equation
Igor Kukavica, Qi Xu
We address analytic regularity for the divergence equation in , with on , where is an arbitrary bounded analytic domain and $\int_Ω f\,…
A global existence result on weak solutions for the 3D Navier-Stokes-plate system with no contact
Mario Bukal, Igor Kukavica, Linfeng Li +1
We consider the three-dimensional fluid-structure interaction system modeling a system consisting of a viscous incompressible fluid and an elastic plate forming its moving upper bo…
A geophysical free-boundary system modeling an ice-sheet interacting with an ocean
Matthias Hieber, Igor Kukavica, Amjad Tuffaha +1
We consider a free-boundary model for the ice-sheet interacting with an ocean. The model captures the coupling between a viscous geophysical fluid and an elastic interface through…
A no-contact result for a plate-fluid interaction system in dimension three
Mario Bukal, Igor Kukavica, Linfeng Li +1
We address the fluid-structure interaction between a viscous incompressible fluid and an elastic plate forming its moving upper boundary in three dimensions. The fluid is described…
The Euler equations with variable coefficients
Benjamin Ingimarson, Igor Kukavica, Amjad Tuffaha
We establish local-in-time existence for the Euler equations on a bounded domain with space-time dependent variable coefficients, given initial data under the optimal…
The structure of weak solutions to the Navier-Stokes equations
Zachary Bradshaw, Igor Kukavica
The existence of superfluous solutions to the Navier-Stokes equations in the whole space implies that not all solutions with uniformly locally bounded energy satisfy a useful local…
Nodal set for the Schrödinger equation under a local growth condition
Igor Kukavica, Linfeng Li
We address the upper bound on the size of the nodal set for a solution of the Schrödinger equation in an open set in , where the coeffic…
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 …
A free boundary inviscid model of flow-structure interaction
Mustafa Sencer Aydın, Igor Kukavica, Amjad Tuffaha
We address the existence and of solutions for the Euler-plate free-boundary system modeling an interaction of a three-dimensional inviscid fluid and an evolving plate. We prove the…
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…
Observability from a measurable set for functions in a Gevrey class
Igor Kukavica, Linfeng Li
We provide an observability inequality in terms of a measurable set for general Gevrey regular functions. As an application, we establish an observability estimate from a measurabl…
Inviscid fluid interacting with a nonlinear two-dimensional plate
Abhishek Balakrishna, Igor Kukavica, Boris Muha +1
We address a moving boundary problem that consists of a system of equations modeling an inviscid fluid interacting with a two-dimensional nonlinear Koiter plate at the boundary. We…
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…
Upper bounds of nodal sets for Gevrey regular parabolic equations
Guher Camliyurt, Igor Kukavica, Linfeng Li
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.…
Euler Equations in Sobolev conormal spaces
Mustafa Sencer Aydın, Igor Kukavica
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 i…
On Green's function of the vorticity formulation for the 3D Navier-Stokes equations
Igor Kukavica, Fei Wang, Yichun Zhu
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 u…
Uniform bounds and the inviscid limit for the Navier-Stokes equations with Navier boundary conditions
Mustafa Sencer Aydın, Igor Kukavica
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 re…
Global-in-time weak solutions for an inviscid free surface fluid-structure problem without damping
Thomas Alazard, Igor Kukavica, Amjad Tuffaha
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-…
On the local existence of solutions to the fluid-structure interaction problem with a free interface
Igor Kukavica, Linfeng Li, Amjad Tuffaha
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^{…
On the interaction between compressible inviscid flow and an elastic plate
Igor Kukavica, Šárka Nečasová, Amjad Tuffaha
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 equati…
On the mass transfer in the 3D Pitaevskii model
Juhi Jang, Pranava Chaitanya Jayanti, Igor Kukavica
We examine a micro-scale model of superfluidity derived by Pitaevskii in 1959 which describes the interacting dynamics between superfluid He-4 and its normal fluid phase. This syst…
Construction of the free-boundary 3D incompressible Euler flow under limited regularity
Mustafa Sencer Aydin, Igor Kukavica, Wojciech S. Ożański +1
We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We construct unique local-in-time solutions in the Lagrangian setting fo…
Small-data global existence of solutions for the Pitaevskii model of superfluidity
Juhi Jang, Pranava Chaitanya Jayanti, Igor Kukavica
We investigate a micro-scale model of superfluidity derived by Pitaevskii in 1959 to describe the interacting dynamics between the superfluid and normal fluid phases of Helium-4. T…