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Jul 20, 2013
07/13

by
Olga Rozanova

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We prove that the smooth solutions to the Cauchy problem for the Navier-Stokes equations with conserved mass, total energy and finite momentum of inertia loses the initial smoothness within a finite time in the case of space of dimension 3 or greater even if the initial data are not compactly supported.

Source: http://arxiv.org/abs/0804.1549v2

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Jun 28, 2018
06/18

by
Olga Rozanova

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We study a possibility of existence of localized two-dimensional structures, both smooth and non-smooth, that can move without significant change of their shape in a leading stream of compressible barotropic fluid on a rotating plane.

Topics: Analysis of PDEs, Mathematics

Source: http://arxiv.org/abs/1507.00690

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Sep 18, 2013
09/13

by
Olga Rozanova

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We present a technique that allows to obtain certain results in the compressible fluid theory: in particular, it is a nonexistence result for the highly decreasing at infinity solutions to the Navier-Stokes equations, the construction of the solutions with uniform deformation and the study of behavior of the boundary of a material volume of liquid.

Source: http://arxiv.org/abs/0707.3467v1

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46

Sep 18, 2013
09/13

by
Tudor Ratiu; Olga Rozanova

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We prove that the smooth solutions to the Cauchy problem for the compressible general three-dimensional Ericksen--Leslie system modeling nematic liquid crystal flow with conserved mass, linear momentum, and dissipating total energy, generally lose classical smoothness within a finite time.

Source: http://arxiv.org/abs/1209.2988v1

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Jul 20, 2013
07/13

by
Olga Rozanova

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We consider solutions to the hyperbolic system of equations of ideal granular hydrodynamics with conserved mass, total energy and finite momentum of inertia and prove that these solutions generically lose the initial smoothness within a finite time in any space dimension $n$ for the adiabatic index $\gamma \le 1+\frac{2}{n}.$ Further, in the one-dimensional case we introduce a solution depending only on the spatial coordinate outside of a ball containing the origin and prove that this solution...

Source: http://arxiv.org/abs/1107.0365v1

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Sep 19, 2013
09/13

by
Mikhail Martynov; Olga Rozanova

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We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed stock price return as a function of the return and time. The behavior of this function depends on the initial stock price return distribution density. In particular, we show that the graph of the conditional expectation of variance is convex downwards near...

Source: http://arxiv.org/abs/1009.5129v3

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46

Sep 22, 2013
09/13

by
Olga Rozanova

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We prove that the smooth solutions to the Cauchy problem for the three-dimensional compressible barotropic magnetohydrodynamic equations with conserved total mass and finite total energy lose the initial smoothness within a finite time. Further, we show that the same result holds for the solution to the Cauchy problem for the multidimensional compressible Navier-Stokes system. Moreover, for the solution with a finite momentum of inertia we get the two-sided estimates of different components of...

Source: http://arxiv.org/abs/0811.4359v1

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51

Sep 22, 2013
09/13

by
David B. Saakian; Olga Rozanova; Andrei Akmetzhanov

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We introduce a new way to study molecular evolution within well-established Hamilton-Jacobi formalism, showing that for a broad class of fitness landscapes it is possible to derive dynamics analytically within the $1/N$-accuracy, where $N$ is genome length. For smooth and monotonic fitness function this approach gives two dynamical phases: smooth dynamics, and discontinuous dynamics. The latter phase arises naturally with no explicit singular fitness function, counter-intuitively. The...

Source: http://arxiv.org/abs/0908.1615v1

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49

Sep 23, 2013
09/13

by
Olga Rozanova

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We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides, including the viscous term, such solutions, no matter how smooth initially, develop a singularity within a finite time. We find a sufficient condition for the singularity formation, "the best sufficient condition", in the sense that one can explicitly...

Source: http://arxiv.org/abs/math/0411652v2

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39

Sep 18, 2013
09/13

by
Mikhail Martynov; Olga Rozanova

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We present an explicit hedging strategy, which enables to prove arbitrageness of market incorporating at least two assets depending on the same random factor. The implied Black-Scholes volatility, computed taking into account the form of the graph of the option price, related to our strategy, demonstrates the "skewness" inherent to the observational data.

Source: http://arxiv.org/abs/1102.5525v1

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Sep 19, 2013
09/13

by
Sergio Albeverio; Olga Rozanova

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It is well known that the solutions to the non-viscous Burgers equation develop a gradient catastrophe at a critical time provided the initial data have a negative derivative in certain points. We consider this equation assuming that the particle paths in the medium are governed by a random process with a variance which depends in a polynomial way on the velocity. Given an initial distribution of the particles which is uniform in space and with the initial velocity linearly depending on the...

Source: http://arxiv.org/abs/0708.2320v3

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44

Sep 22, 2013
09/13

by
Sergio Albeverio; Anastasia Korshunova; Olga Rozanova

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Using a method of stochastic perturbation of a Langevin system associated with the non-viscous Burgers equation we construct a solution to the Riemann problem for the pressureless gas dynamics describing sticky particles. As a bridging step we consider a medium consisting of noninteracting particles. We analyze the difference in the behavior of discontinuous solutions for these two models and the relations between them. In our framework we obtain a unique entropy solution to the Riemann problem...

Source: http://arxiv.org/abs/0908.2084v2

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41

Jul 20, 2013
07/13

by
Sergio Albeverio; Olga Rozanova

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We consider the Langevin equation describing a stochastically perturbed by uniform noise non-viscous Burgers fluid and introduce a deterministic function that corresponds to the mean of the velocity when we keep the value of position fixed. We study interrelations between this function and the solution of the non-perturbed Burgers equation. Especially we are interested in the property of the solution of the latter equation to develop unbounded gradients within a finite time. We study the...

Source: http://arxiv.org/abs/0804.1553v3

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42

Sep 19, 2013
09/13

by
Anastasia Korshunova; Olga Rozanova

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We extend our result of [1] and show that one can associate with the stochastically perturbed non-viscid Burgers equation a system of viscous balance laws. The Cauchy data for the Burgers equation generates the data for this system. Till the moment of the shock formation in the solution to the Burgers equation the above system of viscous balance laws can be reduced to the pressureless gas dynamics system (in a limit as the parameters of perturbation tend to zero). If the solution to the Burgers...

Source: http://arxiv.org/abs/1010.0212v1

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48

Sep 23, 2013
09/13

by
Olga Rozanova

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The question on expansion of moving volume inside of a smooth flow of the compressible liquid is under consideration. We find a condition on initial data such that if it holds, then within a finite time either the boundary of the moving volume attains a given neighborhood of a certain point (that do not belong to the volume initially), or some a priori estimate for the pressure on the boundary of volume fails.

Source: http://arxiv.org/abs/math-ph/0511088v1

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Jun 28, 2018
06/18

by
Olga Rozanova; Jui-Ling Yu; Chin-Kun Hu

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We study the influence of linear friction on the vortex motion in a non-viscous stratified compressible rotating media. Our method can be applied to describe the complex behavior of a tropical cyclone approaching land. In particular, we show that several features of the vortex in the atmosphere such as a significant track deflection, sudden decay and intensification, can be explained already by means of the simplest two dimensional barotropic model, which is a result of averaging over the...

Topics: Fluid Dynamics, Analysis of PDEs, Mathematics, Physics

Source: http://arxiv.org/abs/1507.08308

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Sep 21, 2013
09/13

by
Olga Rozanova

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We consider a generalization of the compressible barotropic Navier-Stokes equations to the case of non-Newtonian fluid in the whole space. The viscosity tensor is assumed to be coercive with an exponent $q>1.$ We prove that if the total mass and momentum of the system are conserved, then one can find a constant $q_0>1$ depending on the dimension of space $n$ and the heat ratio $\gamma$ such that for $q\in [q_0,n)$ there exists no global in time smooth solution to the Cauchy problem. We...

Source: http://arxiv.org/abs/1008.4455v1