arXiv subjects

Krutika Tawri

Publications and source records attributed to Krutika Tawri.

13 recordsLinked to original sources

arXiv2026

Suppression of Blow-up in Two-dimensional Keller--Segel Systems by Stochastic Couette Flows

We study Keller--Segel systems on $ \mathbb{T}\times\mathbb{R}$ subject to a stochastic Couette transport flow. We prove that sufficiently strong mixing suppresses chemotactic finite-time blow-up with high probability; thus yielding a unique global-in-time mild solution for initial data of arbitrary mass. Moreover, we obtain a quantitative estimate for the probability of blow-up, showing that it decays exponentially with increasing strength of the stochastic shear. Our analysis is based on the enhanced dissipation generated by the stochastic shear flow. To prove our main result, we first construct a maximal local mild solution through pathwise estimates for the random solution operator of passive scalar transport equations and a fixed-point argument. To obtain global control, we decompose the evolution into time blocks and exploit mixing-induced decay of the nonzero spatial Fourier modes. A nonlinear bootstrap argument then yields global existence above an almost-sure finite random threshold for the shear strength which is obtained by an application of the Borel-Cantelli theorem.

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arXiv2026

Global Well-posedness of the 2D Stochastic Self-consistent Keller-Segel-Navier-Stokes System with Subcritical Cellular Mass

We consider a stochastic Keller-Segel-Navier-Stokes system in $R^2$ describing the collective motion of cells in an ambient stochastic fluid flow, where the cells are attracted by a chemical substance and transported by the ambient fluid velocity, and the fluid motion is self-consistently driven by forces induced by the cells. We prove the existence of a unique mild solution globally-in-time to the two-dimensional stochastic Keller-Segel-Navier-Stokes system with subcritical mass.

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arXiv2026

Finite-time contact in fluid-elastic structure interaction: Navier-slip coupling condition

We consider a fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the 2D Navier-Stokes equations, through a thin deformable elastic tube, displacement of which is not known a priori. The elastodynamics problem is given by 1D plate equations. The fluid and the structure are nonlinearly coupled via the kinematic and dynamic coupling conditions at the fluid-structure interface. The fluid flow is driven by dynamic pressure data imposed at the inlet and outlet of the tube. We impose the Navier-slip boundary condition at the deformable fluid-structure interface and at the bottom rigid boundary of the fluid domain. Hence, beyond the usual geometric nonlinearities arising from nonlinear coupling in FSI with no-slip, the analysis is more challenging due to the possibility of tangential jumps of the fluid and structural velocities at the moving interface. We first discuss the existence of weak solutions and then establish a `hidden' spatial regularity result for the structure displacement. Our main result proves the existence of a finite time for weak solutions at which the compliant upper boundary meets the lower boundary (i.e., the tube collapses), provided that there is a sufficient pressure drop across the channel. This resolves the ''no-collision'' paradox identified by Grandmont and Hillairet in the no-slip setting in [Arch. Ration. Mech. Anal., 220(3): 1283-1333, (2016)], the counterpart to the present work. To the best of our knowledge, this is the first work that rigorously establishes finite-time contact in a fluid-elastic structure interaction system, thereby validating the model to correctly capture near-contact dynamics.

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arXiv2026

Stochastic Compressible Euler Equations with Frictional Damping: Existence of $L^\infty$ Martingale Solutions and Asymptotic Porous Medium-Like Behavior

We study the one-dimensional isentropic compressible Euler equations with linear (frictional) damping, subject to multiplicative, white-in-time stochastic forcing. The system is posed on a bounded interval with $L^\infty$ initial data and Dirichlet boundary conditions imposed on the momentum. We establish the global-in-time existence of $L^\infty$ martingale solutions that satisfy an appropriate entropy inequality. Then, we analyze the long-time behavior of these solutions and show that, under suitable assumptions on the noise, they converge almost surely and exponentially fast to a constant steady state of the system. The limiting density is well-approximated by the asymptotic solution of the deterministic porous medium equation, while the momentum exhibits the asymptotic behavior predicted by Darcy's law. The analysis in the stochastic setting is delicate, as temporal white-noise perturbations can significantly influence the long-time statistics of the solution. Our approach hinges on deriving sharp moment estimates for the entropy, which enable us to quantify and ultimately prove the decay of stochastic effects. To the best of our knowledge, this work provides the first rigorous pathwise convergence result for the long-time behavior of solutions to the stochastic isentropic compressible Euler equations with linear damping.

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arXiv2026

Well-posedness and existence of an invariant measure for the linearly-damped KdV equations driven by a jump noise

In this paper, we investigate the linearly damped KdV equation on the one-dimensional torus $\mathbb{T}$, perturbed by a multiplicative Lévy noise. For any damping coefficient $γ> 0$, we establish the existence and uniqueness of a pathwise weak solution with values in $H^2(\mathbb{T})$. In the second part of the paper, we analyze the long-time behavior of these solutions. This study is particularly subtle as the presence of jumps in time can significantly influence the asymptotics. We show, using the techniques of Maslowski and Seidler, that, provided the frictional damping coefficient $γ> 0$ is sufficiently large, the system influenced by square-integrable jumps admits an invariant measure in $H^2(\mathbb{T})$.

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arXiv2025

Statistically stationary solutions to the stochastic isentropic compressible Euler equations with linear damping

We study the long time behavior of isentropic compressible Euler equations with linear damping driven by a white-in-time noise, on a one-dimensional torus. We prove the existence of a statistically stationary solution in the class of weak martingale entropy solutions for any adiabatic constant $γ>1$, which satisfies an associated entropy inequality. To establish this result, we use a multi-level approximation scheme consisting of a truncation parameter $R$ and an artificial viscosity parameter $ε$. The truncated system preserves the structure of the regularized system with the artificial viscosity, thereby providing key properties such as an invariant region and non-existence of vacuum at the approximate level. These properties allow us to construct an invariant measure for the approximate system in both $R$ and $ε$ associated to a Feller semigroup for the well-posed dynamics of the approximate system for any $γ> 1$. This gives us a statistically stationary solution for the approximate problem, which we then successively pass to the limit as $R \to \infty$ and as $ε\to 0$ to obtain a statistically stationary solution to the original stochastic system. Our analysis is novel, using new techniques for establishing uniform bounds on entropies of all orders, which allow us to pass to the limit in the parameters. We believe that this result is a valuable step towards further understanding the long-time statistical behavior of the stochastic Euler equations in one spatial dimension.

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arXiv2025

Existence of weak martingale solutions to a stochastic fluid-structure interaction problem with a compressible viscous fluid

We study the existence of weak martingale solutions to a stochastic moving boundary problem arising from the interaction between an isentropic compressible fluid and a viscoelastic structure. In the model, we consider a three-dimensional compressible isentropic fluid with adiabatic constant $γ> 3/2$ interacting dynamically with an elastic structure on the boundary of the fluid domain described by a plate equation, under the additional influence of stochastic perturbations which randomly force both the compressible fluid and elastic structure equations in time. The problem is nonlinearly coupled in the sense that the a priori unknown (and random) displacement of the elastic structure from its reference configuration determines the a priori unknown (and random) time-dependent fluid domain on which the compressible isentropic Navier-Stokes equations are posed. We use a splitting method, consisting of a fluid and structure subproblem, to construct random approximate solutions to an approximate Galerkin form of the problem with artificial viscosity and artificial pressure. We introduce stopped processes of structure displacements which handle the issues associated with potential fluid domain degeneracy. In this splitting scheme, we handle mathematical difficulties associated with the a priori unknown and time-dependent fluid domain by using an extension of the fluid equations to a fixed maximal domain and we handle difficulties associated with imposing the no-slip condition in the stochastic setting by using a novel penalty term defined on an external tubular neighborhood of the moving fluid-structure interface. To the best of our knowledge, this is the first well-posedness result for stochastic fluid-structure interaction with compressible fluids.

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arXiv2024

Existence and Regularity Results for a Nonlinear Fluid-Structure Interaction Problem with Three-Dimensional Structural Displacement

In this paper we investigate a nonlinear fluid-structure interaction (FSI) problem involving the Navier-Stokes equations, which describe the flow of an incompressible, viscous fluid in a 3D domain interacting with a thin viscoelastic lateral wall. The wall's elastodynamics is modeled by a two-dimensional plate equation with fractional damping, accounting for displacement in all three directions. The system is nonlinearly coupled through kinematic and dynamic conditions imposed at the time-varying fluid-structure interface, whose location is not known a priori. We establish three key results, particularly significant for FSI problems that account for vector displacements of thin structures. Specifically, we first establish a hidden spatial regularity for the structure displacement, which forms the basis for proving that self-contact of the structure will not occur within a finite time interval. Secondly, we demonstrate temporal regularity for both the structure and fluid velocities, which enables a new compactness result for three-dimensional structural displacements. Finally, building on these regularity results, we prove the existence of a local-in-time weak solution to the FSI problem. This is done through a constructive proof using time discretization via the Lie operator splitting method. These results are significant because they address the well-known issues associated with the analysis of nonlinearly coupled FSI problems capturing vector displacements of elastic/viscoelastic structures in 3D, such as spatial and temporal regularity of weak solutions and their well-posedness.

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arXiv2024

Existence of martingale solutions to a nonlinearly coupled stochastic fluid-structure interaction problem

In this paper we study a nonlinear stochastic fluid-structure interaction problem with a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a 2D cylinder interacting with an elastic lateral wall whose elastodynamics is described by a membrane/shell equation. The flow is driven by the inlet and outlet data, and by the stochastic forcing. The stochastic noise is applied both to the fluid equations as a volumetric body force, and to the structure as an external forcing to the deformable fluid boundary. The fluid and the structure are nonlinearly coupled via the kinematic and dynamic conditions assumed at the moving interface, which is a random variable not known a priori. The geometric nonlinearity due to the nonlinear coupling requires the development of new techniques to capture martingale solutions for this class of stochastic fluid-structure interaction problems. We introduce a constructive approach based on a Lie splitting scheme and prove the existence of martingale solutions to the system. To the best of our knowledge, this is the first result in the field of stochastic PDEs that addresses existence of solutions on moving fluid domains involving incompressible viscous fluids, where the displacement of the boundary and the fluid domain are random variables that are not known a priori and are parts of the solution itself.

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arXiv2024

A stochastic fluid-structure interaction problem with the Navier slip boundary condition

We prove the existence of martingale solutions to a stochastic fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the Navier-Stokes equations, through a deformable elastic tube modeled by shell/membrane equations. The fluid and the structure are nonlinearly coupled via the kinematic and dynamic coupling conditions at the fluid-structure interface. This article considers the case where the structure can have unrestricted displacement and explores the Navier-slip boundary condition imposed at the fluid-structure interface, displacement of which is not known a priori and is itself a part of the solution. The proof takes a constructive approach based on a Lie splitting scheme. The geometric nonlinearity stemming from the nonlinear coupling, the possibility of random fluid domain degeneracy, the potential jumps in the tangential components of the fluid and structure velocities at the moving interface and the low regularity of the structure velocity require the development of new techniques that lead to the existence of martingale solutions.

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arXiv2024

A 2D stochastic fluid-structure interaction problem in compliant arteries with non-zero longitudinal displacement

In this paper, we study a nonlinear fluid-structure interaction problem driven by a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a 2D cylinder interacting with an elastic wall whose elastodynamics is described by membrane equations. The stochastic force is applied both to the fluid equations as a volumetric body force, and to the structure as an external forcing to the deformable fluid boundary. The fluid and the structure are nonlinearly coupled via the kinematic and dynamic conditions assumed at the moving interface, which is a random variable not known a priori. In particular, we consider the case where the structure is allowed to have non-zero longitudinal displacement.

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arXiv2022

Local well-posedness of a three-dimensional phase-field model for thrombus and blood flow

In this article we consider a fluid-structure interactions model on a three dimensional bounded domain, that describes the mechanical interaction between blood flow and a thrombus with Hookean elasticity. The interface between the two phases is given by a smooth transition layer, diffuse with a finite thickness. We derive various a priori estimates and prove local well-posedness results using the Faedo-Galerkin method.

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arXiv2021

Nonlinear Stochastic parabolic partial differential equations with a monotone operator of the Ladyzenskaya-Smagorinsky type, driven by a Levy noise

The aim of this article is to show the global existence of both martingale and pathwise solutions of stochastic equations with a monotone operator, of the Ladyzenskaya-Smagorinsky type, driven by a general Levy noise. The classical approach based on using directly the Galerkin approximation is not valid. Instead, our approach is based on using appropriate approximations for the monotone operator, Galerkin approximations and on the theory of martingale solutions.

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