3 citations · 4 across the 22 of their papers we have counts for
24 papers · 1 filter
The Lorentz Threshold in Fourier Restriction
R. Shahmurov, V. Shahmurov
Classical Stein--Tomas restriction controls a Fourier transform on a curved surface, but the estimate changes when its values lie in a Banach space. We determine the sharp Lorentz…
-Valued Stein--Tomas Restriction for Schatten Classes
R. Shahmurov, V. Shahmurov
Let be a compact hypersurface with nonvanishing Gaussian curvature. We prove the sharp matrix-dimension-independent Schatten-valued Stein--Tomas range \…
Axisymmetric Navier--Stokes with Swirl: Regularity and Blow-Up Constraints
Rishad Shahmurov
For smooth finite-energy axisymmetric Navier--Stokes solutions with swirl, we give a continuation criterion in terms of the signed cumulative work of the actual post-cut source-gen…
Derivative Embeddings in Vector-Valued Morrey Spaces
Rishad Shahmurov, Veli Shahmurov
We develop an intermediate-derivative theory for Banach-valued evolution classes with Morrey control in time. Let be Banach spaces, , , an…
A Morrey-to-Lebesgue Equivalence for Convolution Calderón--Zygmund Operators
Rishad Shahmurov, Veli Shahmurov
We prove that, for vector-valued convolution Calderón--Zygmund operators, boundedness on a single nontrivial Morrey space is equivalent to the corresponding global boundednes…
Compact Embeddings of Vector-Valued Morrey Spaces
Rishad Shahmurov, Veli Shahmurov
We develop compactness and defect-of-compactness results for Banach-valued evolution classes with Morrey control in time. For \[ \begin{aligned} \mathbb W_M^{p,λ}(0,T;E_0,E_1) =\{u…
Exact Traces for Vector-Valued Morrey Spaces
Rishad Shahmurov, Veli Shahmurov
We establish an exact trace theorem for vector-valued time-Morrey spaces and complementary continuity theorems for time-BMO evolution classes. For a Banach couple $X_1\hookrightarr…
Endpoint Structure in Three-Dimensional Navier--Stokes
Rishad Shahmurov
We study possible singular endpoints of the three-dimensional incompressible Navier--Stokes equations by parabolic rescaling. Weak limits can lose information through pressure, non…
Critical Structure of Axisymmetric Navier--Stokes with Swirl
Rishad Shahmurov
We study the axisymmetric Navier--Stokes equations with swirl in the variables , , and . Their distinct scaling degrees lead to several critical transitio…
Source-Driven Transitions in Axisymmetric Euler Flow
Rishad Shahmurov
We study a finite-time source-driven transition in axisymmetric Euler flow with swirl. For an explicit smooth compact datum, we prove exact source, moment-return, fixed-label trans…
Endpoint Architectures for Navier--Stokes
Rishad Shahmurov
We compare two endpoint analyses for three-dimensional Navier--Stokes flow: a general suitable-weak framework and the axisymmetric equations with swirl. The common backend is selec…
Boundary Hyperbolic Packets in Axisymmetric Euler Flow
Rishad Shahmurov
We study hyperbolic side-wall packets for the axisymmetric Euler equations with swirl in a periodic cylinder. In the exact odd class, and satisfy and $D…
Hardy Criticality in Axisymmetric Swirl
Rishad Shahmurov
For smooth axisymmetric Navier--Stokes flow with swirl, set \(F=u^θ/r\), \(Γ=ru^θ\), \(G=ω^θ/r\), and \(U=u^r/r\). Weighted swirl energies are classical; we determine the sharp two…
Threshold Decomposition of Vorticity Stretching and Palinstrophy
Rishad Shahmurov
We give an exact finite-time decomposition of vortex stretching by resolving the vorticity equation according to the size of the vorticity. For almost every threshold , the st…
Nonlocal Hyperdissipative Perturbations of the Three Dimensional Navier-Stokes System
Veli Shahmurov, Rishad Shahmurov
We study the three-dimensional incompressible Navier-Stokes system on with an additional dissipative nonlocal term \[ \partial_t u + (u\cdot\nabla)u + \nabla p = νΔu…
Axis Regularity in the 5D Corridor
Rishad Shahmurov
We study axisymmetric Navier--Stokes flow with swirl through the five-dimensional lift of the azimuthal-vorticity equation. We prove the weighted identities behind the corridor met…
Critical Compression in Axisymmetric Swirl
Rishad Shahmurov
We study two scale-critical inward-compression mechanisms in smooth axisymmetric Navier--Stokes flow with swirl. For the weighted swirl family Y_d=r^d u^theta, -1<=d<1, an exact L^…
Vorticity-Response Blowup in Axisymmetric Models
Rishad Shahmurov
We study how the orientation and elliptic depth of swirl-generated vorticity response affect singularity formation in axisymmetric model equations. For a sign-reversed Hou--Li mode…
The regularity properties and blow-up for convolution wave equations and applications
Veli Shakhmurov, Rishad Shahmurov
In this paper, the Cauchy problem for linear and nonlinear convolution wave equations are studied.The equation involves convolution terms with a general kernel functions whose Four…
Existence local and global solution of multipoint Cauchy problem for nonlocal nonlinear equations
Veli Shakhmurov, Rishad Shahmurov
In this paper, the multipoint Cauchy problem for nonlocal nonlinear wave type equatıons are studied.The equation involves a convolution integral operator with a general kernel func…
The integral Cauchy problem for generalized Boussinesq equations with general leading parts
Veli Shakhmurov, Rishad Shahmurov
In this paper, the integral initial value problems for Boussinesq type equations are studied. The equation include the general differential operators. The existence, uniqueness and…
Operator-valued multipliers in vector-valued weighted Besov spaces and applications
Veli Shakhmurov, Rishad Shahmurov
The operator-valued multiplier theorems in weighted abstract Besov spaces are studied. These results permit us to show embedding theorems in weighted Besov-Lions type spaces. The m…
Linear and nonlinear convolution operator equations on the infinite strip
Rishad Shahmurov
In the present paper we characterize the existence and uniqueness of maximal Lp-regular solutions of high order convolution operator equations. Particularly, we get coercive unifor…
Lp regularity for convolution operator equations in Banach spaces
Rishad Shahmurov
Here we utilize operator--valued Lq-Lp Fourier multiplier theorems to establish lower bound estimates for large class of elliptic integro-differential equations in Rd. Moreover, we…